TEST BANK for Trigonometry, 5th Edition by Cynthia Young

TEST BANK for Trigonometry, 5th Edition by Cynthia Young

Chapter 1 - 8

Chapter 1 1.1

Right Triangle Trigonometry

Angles, Degrees, and Triangles

1) Specify the measure of the angle in degrees with a 2/5 rotation counterclockwise, to the nearest whole degree.

A) 144° B) 216° C) 59° D) 281° Answer: A Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 2) Specify the measure of the angle in degrees with a 4/9 rotation clockwise, to the nearest whole degree.

A) -160° B) 200° C) 110° D) 160° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 3) Specify the measure of the angle in degrees with a 1/7 rotation clockwise, to the nearest whole degree.

Answer: -51° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 4) Specify the measure of the angle in degrees with a 2/9 rotation counterclockwise, to the nearest whole degree.

Answer: 80° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01

1

5) Find the complement of an angle that measures 70 degrees.

A) 25° B) 110° C) 160° D) 20° Answer: D Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 6) Find the complement of an angle that measures 65 degrees.

Answer: 25° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 7) Find the supplement of an angle that measures 120 degrees.

A) 300° B) 67° C) 60° D) 210° Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 8) Find the supplement of an angle that measures 14 degrees.

Answer: 166° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 9) Find the measure of each angle to one decimal place if angle A measures (10x)° and angle B measures (13x)°.

Answer: 39.1°, 50.9° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01

2

10) Find the measure of each angle to one decimal place if angle A measures (17x)° and angle B measures (14x)°.

Answer: 98.7°, 81.3° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 11) If the measure of angle α = 108° and the measure of angle β = 2°, find the measure of angle γ.

Answer: 70° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 12) If the measure of angle α = 114° and the measure of angle β = 30° find the measure of angle γ.

A) 96° B) 126° C) 36° D) 99° Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01

3

13) If β = γ and α = 3β, find all three angles.

A) 1°, 1°, 178° B) 25°, 25°, 130° C) 40°, 40°, 100° D) 36°, 36°, 108° Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 14) If β = 6γ and α = 13γ , find all three angles.

Answer: 9°, 54°, 117° Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 15) Find two supplementary angles with measures (9x)° and (9x)°. Write your answer to one decimal place.

Answer: 90°, 90° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 16) If d = 4, and e = 7, find f. Express the length exactly.

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01

4

17) If d = 5, and e = 12, find f . Express the length exactly.

Answer: f = 13 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 18) If d = 7, and e = 22, find f in the following right triangle. Write your answer to two decimal places.

Answer: 23.09 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 19) If the hypotenuse of a 45° - 45° - 90° triangle has a length of

, how long are the legs?

Answer: 16 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 20) If the longer leg of a 30° - 60° - 90° triangle has a length of

, how long is the hypotenuse?

Answer: 18 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 21) Clock. What is the measure (in degrees) of the two angles between the hour hand and minute 5

hand on a clock when the time is exactly 2:22? Assume the hour hand points to 2:00.

A) 120°, 240° B) 72°, 288° C) 132°, 228° D) 12°, 348° Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 22) Clock. What is the measure (in degrees) of the two angles between the hour hand and minute hand on a clock when it is exactly 4:33? Assume the hour hand points to 4:00.

Answer: 78°, 282° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 23) Ferris Wheel. The Ferris Wheel was an amusement park ride that was invented by bridge builder George W. Ferris, and unveiled at the 1889 Paris Exhibition. The wheel had a diameter of 250 feet, a circumference of 825 feet, and a maximum height of 264 feet. If the Ferris Wheel made one rotation in 40 minutes, what was the measure of the angle (in degrees) that a cart on the Wheel would rotate in 26 minutes?

A) 260° B) 234° C) 208° D) 182° Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01

6

24) Ferris Wheel. The Ferris Wheel was an amusement park ride that was invented by bridge builder George W. Ferris, and unveiled at the 1889 Paris Exhibition. The wheel had a diameter of 250 feet, a circumference of 825 feet, and a maximum height of 264 feet. If the Ferris Wheel made one rotation in 40 minutes, what was the measure of the angle (in degrees) that a cart on the Wheel would rotate in 15 minutes?

Answer: 135° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 25) Roof Truss. A roofing contractor is building triangular trusses with a pitch of 45 degrees. If the hypotenuse of the trusses is 101 feet, what is the number of linear feet of board required to build each truss (to the nearest foot)?

101 ft A) 244 linear feet B) 276 linear feet C) 143 linear feet D) 387 linear feet Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 26) Roof Truss. A roofing contractor is building triangular roof trusses with a pitch of 45 degrees.

If the hypotenuse of the trusses is 141 feet, what is the number of linear feet of board required to build each truss (to the nearest foot)?

141 ft Answer: 340 linear feet Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01 7

27) A rope is to be tied from the top of a tent 8 feet high to a stake in the ground. If the angle between the ground and the rope is to be 31°, how far from the base of the tent should the rope be staked? (Round to two decimal places.)

A) 9.33 feet B) 13.31 feet C) 4.12 feet D) 15.53 feet Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 01 28) If a revolving restaurant can rotate 40° in 45 minutes, how long does it take for the restaurant to make a complete revolution?

Answer: 405 minutes Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 01

8

Trigonometry, 5e (Young) Chapter 1 Right Triangle Trigonometry 1.2

Similar Triangles

1) Find the measure of angle C if angle H is 69°.

A) 21° B) 159° C) 69° D) 111° Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 2) Find the measure of angle E if angle A is 131°.

A) -41° B) 221° C) 131° D) 49° Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02

9

3) If the measure of angle E is (5x)° and angle D is (9x - 48)°, what is the measure of angle E to the nearest degree?

A) 60° B) 4° C) 48° D) 120° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 4) If the measure of angle D is (4x)° and angle F is (2x - 42)°, what is the measure of angle G to the nearest degree?

A) 32° B) 148° C) 37° D) 116° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02

10

5) If the measure of angle H is (2x)° and angle D is (5x - 201)°, what is the measure of angle H to the nearest degree?

Answer: 134° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 02 6) If the measure of angle D is (8x)° and angle C is (3x - 29)°, what is the measure of angle G to the nearest degree?

Answer: 28° Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 7) If the measure of angle D is (4x)° and angle G is (6x - 100)°, what is the measure of angle E to the nearest degree?

Answer: 112° Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02

11

8) What type of triangle is shown here?

A) Isosceles Triangle (non-right) B) Right Triangle (non-isosceles) C) Isosceles Right Triangle D) Acute Scalene Triangle Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 9) What type of triangle is shown here?

A) Equilateral Triangle B) Obtuse Isosceles Triangle C) Acute Isosceles Triangle D) Obtuse Scalene Triangle Answer: B Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 10) Calculate the length of F, given that the two triangles are similar and A = 4, C = 6, and D = 8.

Round your answer to two decimal places if needed.

Answer: 12 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 02

12

11) Calculate the length of F given that the two triangles are similar and A = 8, C = 13, and D = 7.

A) 11.4 B) 4.3 C) 14.9 D) 6 Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 12) Calculate the length of F, given that the two triangles are similar and A = 16, C = 19, and Round your answer to two decimal places if needed.

Answer: 9.5 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 02 13) Height of a light pole. At a certain time in the afternoon a light pole casts a shadow that is 79 inches long. At the same time, a woman of height 67 inches casts a shadow that is 74 inches long.

How tall is the light pole?

A) 62.8 inches B) 87.3 inches C) 71.5 inches D) 71.6 inches Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02

13

14) Height of a palm tree. A palm tree casts a shadow that is 47.7 feet long. At the same time, a man of height 69.1 inches casts a shadow that is 73.6 inches long. How tall is the palm tree?

A) 106.6 feet B) 44.8 feet C) 50.8 feet D) 71.6 feet Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02 15) Height of a highway sign. At a certain time in the afternoon a highway sign casts a shadow that is 137.7 inches long. At the same time, a woman of height 61.4 inches casts a shadow that is 26.4 inches long. How tall is the highway sign to one decimal point?

Answer: 320.3 inches Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 02 16) The Great Pyramid of Giza. The Great Pyramid of Giza was one of the Seven Wonders of the Ancient World. The base of the pyramid is 230 meters on each side and it is 145.5 meters high.

If a child of height 1 meter casts a shadow of 2.6 meters, how far beyond the base of the pyramid does the pyramid's shadow extend? Round your answer to one decimal place.

Answer: 263.3 meters Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 02 17) On a roadmap of the state of New York, a length of one-half inch represents approximately 5.5 miles. How many miles did a highway patrolman travel if the length on the map was 16 inches?

A) 192 miles B) 160 miles C) 88 miles D) 176 miles Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 01, Sec 02

14

18) On an architect's drawing for an office building, 0.25 inches represents 9 feet. If the length of a wall on the architect's drawing is 9.3 inches, what is the length of the wall to one decimal place?

Answer: 334.8 inches Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 01, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

15

Trigonometry, 5e (Young) Chapter 2 Trigonometric Functions 2.1

Angles in the Cartesian Plane

1) State in which quadrant the terminal side of a 1202° angle in standard position lies.

A) QII B) QI C) QIV D) QIII Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01 2) State on what axis the terminal side of a 90° angle in standard position lies.

A) Negative x-axis B) Negative y-axis C) Positive y-axis D) Positive x-axis Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01 3) State in which quadrant the terminal side of a -156° angle in standard position lies.

A) QIII B) QII C) QI D) QIV Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01 4) State on what axis the terminal side of a -990° angle in standard position lies.

A) Negative x-axis B) Negative y-axis C) Positive y-axis D) Positive x-axis Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01

16

5) What angle is coterminal to 585°?

A) 1125° B) 855° C) 1665° D) 405° Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01 6) Name the angle that is coterminal with 280° after making 3 rotations in the counterclockwise direction.

Answer: 1,360° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01 7) Determine the angle of the smallest possible positive measure that is coterminal with 1219°.

A) 162 B) 139 C) 115 D) 104 Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01 8) Determine the angle of the smallest possible positive measure that is coterminal with 1,159°.

Answer: 79° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01 9) Clock. What is the measure of the angle an hour hand on a clock makes if it starts at 3:00 am on Tuesday and continues until 3:00 am on Thursday?

A) -720° B) 1440° C) 720° D) -1440° Answer: D Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01

17

10) Clock. What is the measure of the angle an hour hand on a clock makes if it starts at 3:00 am on Monday and continues until 8:00 pm on Tuesday?

Answer: -1,230° Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01 11) Satellites. Two satellites orbiting the Earth are travelling on the same path but in opposite directions. If they start at the same spot and then sweep through angles of -425° and 2095° before stopping, will they end up at the same spot? Assume they don't collide when they meet on the path.

A) Yes B) No C) Not enough information Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01 12) Electrons. Two electrons orbiting an atom's nucleus are travelling on the same path but in opposite directions. If they start at the same spot and then sweep through angles of -812° and 2,763° before stopping, will they end up at the same spot? Assume they don't collide when they meet on the path.

Answer: No Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01 13) Kite. Henry is flying a kite on the beach. He lets out 68 feet of string and has it flying at an angle of 30° to the ground. How far is the kite extended horizontally and vertically from Henry?

Give the exact answer.

Answer: 34 feet horizontal and 34 feet vertical Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01 14) Ferris Wheel. If the Ferris Wheel is centered at the origin and travels in a counterclockwise direction. A car starts at (0, -100) and before completing 4 rotations it is stopped at Through what angle has the car rotated?

Answer: 1,290° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01

18

15) Ferris Wheel. If the Ferris Wheel is centered at the origin and travels in a counterclockwise direction. A car starts at (0, -100) and before completing 3 rotations it is stopped at Through what angle has the car rotated?

A) 1200° B) 870° C) 930° D) 1230° Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 01

19

16) Sketch the angle with the measurement of 1200° in standard position.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 01 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

20

Trigonometry, 5e (Young) Chapter 2 Trigonometric Functions 2.2

Definition 2 of Trigonometric Functions: The Cartesian Plane

1) The terminal side of an angle θ in standard position passes through the point the exact value of cos θ.

Calculate

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 2) The terminal side of an angle θ in standard position passes through the point the exact value of cos θ.

Calculate

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 3) The terminal side of an angle θ in standard position passes through the point Calculate the exact value of csc θ.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 4) The terminal side of an angle θ in standard position passes through the point the exact value of csc θ.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02

21

Calculate

5) The terminal side of an angle θ in standard position passes through the point the exact value of cot θ.

Calculate

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 6) The terminal side of an angle θ? in standard position passes through the point Calculate the exact value of csc θ.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 7) The terminal side of an angle θ in standard position passes through the point Calculate the exact value of cos θ.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 8) The terminal side of an angle θ in standard position passes through the point ( Calculate the exact value of cos θ.

,-

).

,-

).

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 9) The terminal side of an angle θ in standard position passes through the point ( Calculate the exact value of sec θ.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02

22

10) The terminal side of an angle θ in standard position passes through the point

.

Calculate the value of sin θ.

Answer:

-

Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 11) The terminal side of an angle θ in standard position passes through the point

. Calculate

the value of cos θ.

Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 12) The terminal side of an angle θ in standard position passes through the point

.

Calculate the value of tan θ.

Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 13) The terminal side of an angle θ in standard position passes through the point Calculate the value of cot θ.

Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02

23

.

14) The terminal side of an angle θ in standard position passes through the point

. Calculate

the value of csc θ.

Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 15) The terminal side of an angle θ in standard position passes through the point

.

Calculate the value of sec θ.

Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 16) The terminal side of an angle θ in standard position passes through the point (1, 2). Calculate the value of sin θ. Round your answer to four decimal places.

Answer: 0.8944 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 17) The terminal side of an angle θ in standard position passes through the point (-7, -2). Calculate the value of cos θ. Round your answer to four decimal places.

Answer: -0.9615 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 18) The terminal side of an angle θ in standard position passes through the point (6, -7). Calculate the value of tan θ. Round your answer to four decimal places.

Answer: -1.1667 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 19) The terminal side of an angle θ in standard position passes through the point (6, -2). Calculate the value of cot θ. Round your answer to four decimal places.

Answer: -3.0000 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 24

20) The terminal side of an angle θ in standard position passes through the point (2, -7). Calculate the value of csc θ. Round your answer to four decimal places.

Answer: -1.0400 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 21) The terminal side of an angle θ in standard position passes through the point (-8, -5). Calculate the value of sec θ. Round your answer to four decimal places.

Answer: -1.1792 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 22) Calculate sin θ if the terminal side of θ is defined by the line y = -3x, x ≤ 0, and θ is the smallest positive angle in standard position.

A) B) C) 3 D) Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 23) Calculate sin θ if the terminal side of θ is defined by the line y = -11x, x ≥ 0, and θ is the smallest positive angle in standard position.

Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02

25

24) Calculate sin θ if θ is in standard position and has a measure of 1170°.

A) 0 B) -1 C) 1 D) Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 25) Calculate csc θ if θ is in standard position and has a measure of 3,330°.

Answer: 1 Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 26) A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of ∠ θ drawn in standard position. If tan θ =

A) B) C) D) Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02

26

, then what is sin θ?

27) A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of ∠ θ drawn in standard position. If tan θ =

A) B) C) D) Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02

27

, then what is cos θ?

28) A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of ∠ θ drawn in standard position. If sin θ =

, then what is tan θ?

A) B) C) D) Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 29) A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of ∠ θ drawn in standard position. If tan θ =

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02

28

, then what is sin θ?

30) A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of ∠ θ drawn in standard position. If tan θ =

, then what is cos θ?

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 31) A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of ∠ θ drawn in standard position. If sin θ =

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02

29

, then what is tan θ?

32) Let ∠ θ be the angle of elevation from a point on the ground to the top of a building. If and the distance from the point on the ground to the base of the building is how high is the building? Round the answer to one decimal place.

A) 90.0 feet B) 76.0 feet C) 96.8 feet D) 46.6 feet Answer: D Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 33) Let ∠ θ be the angle of elevation from a point on the ground to the top of a cliff. If and the height of the cliff is 91 feet, how far is the point on the ground to the base of the cliff?

Round the answer to one decimal place.

Answer: 50.3 feet Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 34) Angelina spikes a volleyball such that if θ is the angle of depression for the path of the ball, then

If the ball is hit from a height of 7.6 feet, how far does the ball travel before

hitting the ground? Round the answer to one decimal place.

A) 6.8 feet B) 5.3 feet C) 10.8 feet D) 6.7 feet Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 30

35) Nicole spikes a volleyball such that if θ is the angle of depression for the path of the ball, then cos θ =

. If the ball is hit from a height of 9.3 feet, how far does the ball travel before hitting

the ground? Round the answer to one decimal place.

Answer: 7.9 feet Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 02, Sec 02 36) Calculate the exact value of sin θ when θ is an angle in standard position, if the terminal side of θ lies on the line y = -

x.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 37) Calculate the exact value of cos θ when θ is an angle in standard position, if the terminal side of θ lies on the line y =

x.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 38) Calculate the exact value of csc θ when θ is an angle in standard position, if the terminal side of θ lies on the line y = Answer:

x.

-

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 02, Sec 02 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

31

Trigonometry, 5e (Young) Chapter 3 Radian Measure and the Unit Circle Approach 3.1

Radian Measure

1) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 7 mm.

A) 0.9 radians B) 1.2 radians C) 42.0 radians D) 1.0 radians Answer: B Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 2) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 4.7 cm.

A) 1.7 radians B) 3.5 radians C) 38.5 radians D) 0.6 radians Answer: D Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 3) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 2 ft.

A)

radians

B) 4 radians C)

radians

D)

radians

Answer: B Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01

32

4) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 7 mm. Round your answer to two decimal places.

Answer: 0.88 radians Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 5) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 1.6 yds. Round your answer to two decimal places.

Answer: 0.22 radians Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 6) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length Answer:

m.

radians

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 7) Convert 212 degrees to radians.

A) 3.70π radians B) 0.85π radians C) 1.18π radians D) 2.67π radians Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 8) Convert 344 degrees to radians. Round numbers to two decimal places and leave the answer in terms of π.

Answer: 1.91π radians Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01

33

9) Convert

π radians to degrees.

A) 90.0° B) 0.5° C) 1.8° D) 360.0° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 10) Convert

π radians to degrees. Round the answer to one decimal place.

Answer: 90.0° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 11) Convert 12.7 radians to degrees.

A) 44.53° B) 39.90° C) 0.66° D) 727.66° Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 12) Convert 12.6 radians to degrees. Use 3.14 for π and round the answer to the nearest hundredth of a degree.

Answer: 722.29° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 13) Convert 118.8° to radians.

A) 1.38 radians B) 2.38 radians C) 4.15 radians D) 2.07 radians Answer: D Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

34

14) Convert 236.9° to radians. Round your answer to 3 significant digits.

Answer: 4.13 radians Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 15) Find the reference angle for A)

radians, 40°

B)

radians, 40°

C)

radians, 80°

D)

radians, 80°

in terms of both radians and degrees.

Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 16) Find the reference angle for Answer:

in terms of both radians and degrees.

radians, 20°

Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

35

17) Find the exact value of sin

.

A) 1 B) C) D) Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 18) Find the exact value of csc

.

A) - 2 B) C) D) Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

36

19) Find the exact value of cot

.

A) B) C) D) Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 20) Find the exact value of cos

.

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 21) Find the exact value of csc

.

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 22) Find the exact value of tan

.

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

37

23) Electronic Signals. Two electronic signals that cancel each other out are said to be 180° out of phase, or the difference in their phases is 180°. How many radians out of phase are two signals whose phase difference is 132°?

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 24) Architecture. A citrus fruit stand in California is in the shape of an orange that is cut in half. If a wedge or sector of the orange has a central angle of 255°, how many radians does this represent?

A)

radians

B)

radians

C)

radians

D)

radians

Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 25) Fruit. When a grapefruit is cut in half, wedges or sectors are visible. If the central angle of a sector is 55°, how many radians does this represent?

Answer:

radians

Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 26) Clock. How many radians does the second hand of a clock sweep through in 8 A) 9π radians B) 16π radians C) 25π radians D) 17π radians Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

38

minutes?

27) Clock. How many radians does the second hand of a clock sweep through in 6

minutes?

Answer: 13π radians Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 01 28) Stratosphere Tower. The Stratosphere Tower in Las Vegas dominates the city's landscape by rising 1,149 feet above the desert floor. The restaurant at the top of the tower turns slowly and completes a full revolution in one hour. How many radians will the restaurant have rotated in 98 minutes?

A)

radians

B)

radians

C)

radians

D)

radians

Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 29) Stratosphere Tower. The Stratosphere Tower in Las Vegas dominates the city's landscape by rising 1,149 feet above the desert floor. The restaurant at the top of the tower turns slowly and completes a full revolution in one hour. How many radians will the restaurant have rotated in 78 minutes?

Answer:

radians

Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

39

30) Sprinkler: A sprinkler is set to reach an arc of 47 feet, 19 feet from the sprinkler. Through how many radians does the sprinkler rotate?

A) B) 893 C) 142 D) Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 31) Sprinkler: A sprinkler is set to reach an arc of 15 feet, 9 feet from the sprinkler. Through how many radians does the sprinkler rotate?

Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 32) Electronic Signals. Two electronic signals that cancel each other out are said to be 180° out of phase, or the difference in their phases is 180°. How many radians out of phase are two signals whose phase difference is 27°?

A) B) 21π C) 20π D) Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

40

33) Convert -

π radians to degrees.

A) -112.5° B) -0.2° C) 4.5° D) -288.0° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 34) Convert -87.1° to radians.

A) 1.52 radians B) -3.25 radians C) -3.04 radians D) -1.52 radians Answer: D Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01 35) Find the reference angle for Answer:

in terms of both radians and degrees.

radians, 40°

Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Trigonometry, 5e (Young) 41

Chapter 3 3.2

Radian Measure and the Unit Circle Approach

Arc Length and Area of a Circular Sector

1) Find the exact length of the arc subtended by a central angle of θ = 16 on a circle with radius A) 176 cm B)

cm

C)

cm

D) 27 cm Answer: A Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 2) Find the exact length of the arc subtended by a central angle of θ = yds.

A) 39 yds B)

yds

C)

yds

D) 380 yds Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02

42

on a circle with radius 19

3) Find the exact length of the arc subtended by a central angle of θ = 100° on a circle with radius A) 25 m B)

m

C)

m

D) 100 m Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 4) Find the exact length of the arc subtended by a central angle of θ = 11 radians on a circle with radius 23 m.

Answer: 253 m Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02 5) Find the exact length of the arc subtended by a central angle of θ =

Answer:

on a circle with radius

cm

Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02 6) Find the exact length of the arc subtended by a central angle of θ = 1,800° on a circle with radius Answer: 90 yds Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02

43

7) Find the exact length of the radius of a circle given arc length s =

A)

m

B)

m

C)

m

D)

m

m and central angle

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 8) Find the exact length of the radius of a circle given arc length s =

Answer:

mi

Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02

44

mi and central angle

9) Find the exact length of the radius of a circle given arc length s =

A)

m

B)

m

C)

m

D)

m

m and central angle

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 10) Find the exact length of the radius of a circle given arc length s =

Answer:

ft and central angle

ft

Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 11) Use a calculator to approximate the length of the arc on a circle with central angle radians and radius r = 6 yds.

A) 0.50 yds B) 18.00 yds C) 2.00 yds D) 9.00 yds Answer: B Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02

45

12) Use a calculator to approximate the length of the arc on a circle with central angle θ =

and

radius r = 2.5 ft.

A) 2.4 ft B) 24 ft C) 6.5 ft D) 11 ft Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 13) Use a calculator to approximate the length of the arc on a circle with central angle and radius A) 17 cm B) 13 cm C) 22 cm D) 6 cm Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 14) Use a calculator to approximate the length of the arc on a circle with central angle θ = 0.7 radians and radius r = 9.8 in. Round your answer to two significant digits.

Answer: 6.86 in Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02 15) Use a calculator to approximate the length of the arc on a circle with central angle θ =

and

radius r = 3.9 in. Round your answer to two significant digits.

Answer: 4.6 in Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02 16) Use a calculator to approximate the length of the arc on a circle with central angle θ = 334° and radius r = 30 mm. Round your answer to the nearest integer.

Answer: 175 mm Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02

46

17) Find the area of the circular sector with a radius r = 1.7 in and central angle θ =

.

A) 6.7 B) 13.4 C) 2.1 D) 3.9 Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 18) Find the area of the circular sector with a radius r = 5.4 ft and central angle θ =

.

Answer: 10.2 Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 19) Find the area of the circular sector with a radius r = 4.7 in and central angle θ = 135°.

A) 26.0 B) 52.0 C) 8.3 D) 5.5 Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 20) Find the area of the circular sector with a radius r = 2.9 mm and central angle θ = 140°.

Answer: 10.3 Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02

47

21) Low Earth Orbit Satellites. A low earth orbit (LEO) satellite is traveling in an approximately circular orbit 100 km above the surface of the Earth. If a ground station tracks the satellite when it is within a 72° cone above the tracking antenna (directly overhead), how many kilometers does the satellite travel during the ground station track? Assume the Earth has a radius of 6,400 km.

A) 8042 km B) 2600 km C) 8168 km D) 5445 km Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 22) Low Earth Orbit Satellites. A low earth orbit (LEO) satellite is traveling in an approximately circular orbit 100 km above the surface of the Earth. If a ground station tracks the satellite when it is within a 59° cone above the tracking antenna (directly overhead), how many kilometers does the satellite travel during the ground station track? Assume the Earth has a radius of 6,400 km.

Answer: 6,693 km Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 23) Clock Tower. The Metropolitan Life Insurance Company tower in New York City has clocks on all four sides. If each clock has a minute hand that is 13.25 feet in length, how far does the tip of each hand travel in 25 minutes?

A) 34.7 feet B) 11.6 feet C) 17.3 feet D) 23.1 feet Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 24) Big Ben. The Big Ben clock tower in London has clocks on all four sides. If each clock has a minute hand that is 11.5 feet in length, how far does the tip of each hand travel in 34 minutes?

Round to the nearest integer.

Answer: 41 feet Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02

48

25) Gears. Two gears have interlocking teeth, which cause them to rotate in opposite directions.

The smaller (pinion) gear has a radius of and the larger (spur) gear has a radius of If the pinion gear rotates 88°, how many degrees will the spur gear rotate?

A) 8° B) 161° C) 48° D) 96° Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 26) Gears. Two gears have interlocking teeth, which cause them to rotate in opposite directions.

The smaller (pinion) gear has a radius of and the larger (spur) gear has a radius of If the pinion gear rotates 88°, how many degrees will the spur gear rotate?

Answer: 70° Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 03, Sec 02 27) Windshield Wipers. A windshield wiper that is 11 inches long (blade and arm) rotates 67°.

If the rubber part is 7 inches long, what is the area cleared by the wiper? Round to the nearest square inch.

Answer: 61 square inches Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02 28) Use a calculator to approximate the length of the radius of a circle with central angle θ = 64° and arc length s = 37 in. Round your answer to the nearest integer.

Answer: 33 in Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 03, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Trigonometry, 5e (Young) 49

Chapter 4 4.1

Graphing Trigonometric Functions

Basic Graphs of Sine and Cosine Functions: Amplitude and Period

1) State the amplitude and period of the sinusoidal function. y = -5 cos 15 x Amplitude is ________ Period is ________ Answer: Amplitude is 5 Period is 2π/15 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 2) State the amplitude and period of the sinusoidal function. y=-

sin 10 x

Amplitude is ________ Period is ________ Answer: Amplitude is Period is Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 3) State the amplitude and period of the sinusoidal function. y = 6cos

x

Amplitude is ________ Period is ________ Answer: Amplitude is 6 Period is 14 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

50

4) State the amplitude and period of the sinusoidal function. y=

sin

x

Amplitude is ________ Period is ________ Answer:

Amplitude =

Period =

π

Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 5) State the amplitude and period of the sinusoidal function. y = 6 sin

x

Amplitude is ________ Period is ________ Answer: Amplitude is 6 Period is 6 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 6) Graph the function y = -5 sin x over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

51

7) Graph the function y = sin 8x over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 8) Graph the function y = -cos

over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

52

9) Graph the function y =

over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 10) Find an equation of the graph.

A) y = 2.5 cos B) y = -2.5 cos C) y = 2.5 sin D) y = 2.5 sin Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

53

11) Graph the function y = -2.5 sin

over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 12) Graph the function y = 2 cos

over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

54

13) Graph the function y = -4 sin

over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 14) Graph the function y = -4.5 cos (2πx) over one period.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

55

15) Graph the function y = -cos

over the interval [-8π?, 8π?].

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 16) Graph the function y = -6 cos

over the interval [-16, 16].

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

56

17) Graph the function y = -sin(5π) over the interval [-0.8, 0.8].

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 18) Graph the function y = -cos(7x) over the interval [-4π/7, 4π/7] where 2π/7 is the period of the function.

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

57

19) Find the cos equation of the graph.

Answer:

y = 1.5 cos

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 20) Find the sin equation of the graph.

A) y = 2 sin B) y = -2 sin C) y = 2 cos D) y = 2 cos Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

58

21) Find the cos equation of the graph.

Answer:

y = 3 cos

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 22) Find an equation of the graph.

A) y = sin B) y = -sin C) y = cos D) y = cos Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

59

23) Find the cos equation for the graph.

Answer:

y = -3 cos

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 24) Find an equation for the graph.

A) y = -2.5 cos B) y = 2.5 cos C) y = 2.5 sin D) y = 2.5 sin Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

60

25) Find an equation of the graph.

Answer:

y = -sin

Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 26) Find an equation of the graph.

A) y = -1.5 sin B) y = 1.5 sin C) y = -1.5 cos D) y = -1.5 cos Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

61

27) Find an equation for the graph.

Answer: y = -3.5 cos (2πx) Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 28) Find an equation for the graph.

A) y = 4 cos (2πx) B) y = 4 sin (2πx) C) y = -4 cos (2πx) D) y = 4 sin Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

62

29) What is the frequency for the oscillation modeled by y = 8.5 cos

Frequency is ________ cycles per second Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 30) What is the frequency for the oscillation modeled by y = 6 cos Frequency is ________ cycles per second A) Frequency is

cycles per second

B) Frequency is 18π cycles per second C) Frequency is

cycles per second

D) Frequency is 9π cycles per second Answer: A Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 31) If a sound wave is represented by y = 0.005 cos

, what is amplitude and frequency?

Amplitude is ________ cm Frequency is ________ hertz Answer: Amplitude is 0.005 cm Frequency is 523 hertz Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 32) If a sound wave is represented by y = 0.009 cos 750πt, what is the frequency?

A) Frequency is 375 hertz B) Frequency is 750 hertz C) Frequency is 375π hertz D) Frequency is 750π hertz Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 63

33) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the plane is flying at Mach 2.4? Round to the nearest meter.

Speed of the plane is ________ m/sec.

Answer: 792 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 34) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the plane is flying at Mach 2.8?

Speed of the plane is ________ m/sec.

A) Speed of the plane is 924 m/sec.

B) Speed of the plane is 118 m/sec.

C) Speed of the plane is 0.008 m/sec.

D) Speed of the plane is 92.4 m/sec.

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 35) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the mach number if the plane is flying at 726 m/sec.?

Answer: 2.2 Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01

64

36) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the Mach number if the plane is flying at 495 m/sec.? mach number is ________.

A) Mach number is 1.5 B) Mach number is 0.15 C) Mach number is 15 D) Mach number is0.67 Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 37) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the cone angle is 40°. Round to the nearest whole number.

Speed of the plane is ________ m/sec.

Answer: Speed of the plane is 965 m/sec.

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01 38) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then sin

=

=

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the cone angle is 45°. Round to the nearest whole number.

Speed of the plane is ________ m/sec.

A) Speed of the plane is 862 m/sec.

B) Speed of the plane is 467 m/sec.

C) Speed of the plane is 126 m/sec.

D) Speed of the plane is 281 m/sec.

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 01 65

39) A weight hanging on a spring will oscillate up and down about its equilibrium position after it's pulled down and released. This is an example of simple harmonic motion. This motion would continue forever if there wasn't any friction or air resistance. Simple harmonic motion can be described with the function

where A is the amplitude, t is the time in seconds, m is

the mass and k is a constant particular to that spring. If a spring is measured in centimeters and the weight in grams, then what are the amplitude and mass if

Amplitude: ________ cm.

Mass: ________ g.

Answer: Amplitude: 11 cm.; mass: 47.61 g.

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

66

?

40) A weight hanging on a spring will oscillate up and down about its equilibrium position after it's pulled down and released. This is an example of simple hormonic motion. This motion would continue forever if there wasn't any friction or air resistance. Simple harmonic motion can be described with the function

where A is the amplitude, t is the time in seconds, m is

the mass and k is a constant particular to that spring. If a spring is measured in centimeters and the weight in grams, then what are the amplitude and mass if y = 5.5cos (1.2t )?

Amplitude: ________ cm.

Mass: ________ g.

A) Amplitude: 5.5 cm.; mass:

g.

B) Amplitude: 5.5 cm.; mass:

g.

C) Amplitude: 30.25 cm.; mass:

g.

D) Amplitude: 30.25 cm.; mass: 1.44 g.

Answer: A Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Trigonometry, 5e (Young) 67

Chapter 4 4.2

Graphing Trigonometric Functions

Translations of the Sine and Cosine Functions: Addition of Ordinates

1) State the amplitude, period, and phase shift of the function. y = 5sin(πx + 1) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 5 Period = 2 Phase Shift = Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 2) State the amplitude, period, and phase shift of the function. y = 3sin(πx - 6) A) Amplitude = 3; period = 2π; phase shift = B) Amplitude = 3; period = 2; phase shift = C) Amplitude = 3; period = 2π; phase shift = D) Amplitude = 3; period = 2, phase shift = 6 Answer: B Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

68

3) State the amplitude, period, and phase shift of the function. y = 5cos(10x + π) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 5 Period = Phase Shift = Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 4) State the amplitude, period, and phase shift of the function. y = 10sin(6 + π) A) Amplitude = 10; period =

; phase shift = -

B) Amplitude = -10; period = 3; phase shift = C) Amplitude = 10; period =

; phase shift = -

D) Amplitude = -10; period =

; phase shift =

Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

69

5) State the amplitude, period, and phase shift of the function. y = 10cos(20 + π) Answer: Amplitude = 10 period = phase shift = Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 6) State the amplitude, period, and phase shift of the function. y = 4cos(9x - π) A) Amplitude = 4; period =

; phase shift =

B) Amplitude = 4; period = 9; phase shift = C) Amplitude = -4; period =

; phase shift = -

D) Amplitude = 4 period =

; phase shift =

Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

70

7) State the amplitude, period, and phase shift of the function. y = 9cos(14x - 13) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 9 Period = Phase Shift = Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 8) State the amplitude, period, and phase shift of the function. y = -9sin(18x - 17) A) Amplitude = 9: period =

; phase shift =

B) Amplitude = 9: period =

; phase shift =

π

C) Amplitude = 9: period = 18; phase shift = D) Amplitude = 9: period =

; phase shift =

π

Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

71

9) State the amplitude, period, and phase shift of the function. y = 3cos(17x - 18) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 3 period = phase shift = Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 10) State the amplitude, period, and phase shift of the function. y = 7cos(9x - 10) A) Amplitude = 7; period =

; phase shift =

B) Amplitude = 7; period =

; phase shift = -

C) Amplitude = 7; period =

; phase shift =

π

D) Amplitude = -7; period = 9; phase shift = Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

72

11) State the amplitude, period, and phase shift of the function. y = 3sin

Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 3 period = 16 phase shift = -6 Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 12) State the amplitude, period, and phase shift of the function. y = 5cos A) Amplitude = 5; period = 10; phase shift = -2π B) Amplitude = 5; period = 5; phase shift =

π

C) Amplitude = -5; period = 10; phase shift = 2 D) Amplitude = 5; period = 10; phase shift = -2 Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

73

13) Sketch the graph of the function y =

+

cos

over [-4π, 4π].

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 14) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

+

cos

B) y =

-

cos

C) y =

+

cos

D) y =

+

sin

Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

74

15) Sketch the graph of the function

-

over [-4π, 4π].

cos

Answer:

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 16) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

+

cos

B) y =

-

cos

C) y =

-

cos

D) y =

-

sin

Answer: B Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

75

17) Sketch the graph of the function

+

over [-4π, 4π].

sin

Answer:

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 18) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

-

cos

B) y =

+

cos

C) y =

+

sin

D) y =

+

cos

Answer: D Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

76

19) Sketch the graph of the function y =

-

sin

over [-4π, 4π].

Answer:

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 20) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

-

B) y = C) y = D) y = -

cos -

-

cos cos

-

cos

Answer: A Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

77

21) Sketch the graph of the function y =

+

sin(2x - π)

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 22) Sketch the graph of the function y = 3 - 4sin(5x) over one period starting at

Answer:

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02 78

23) Match the graph of the sine function to the equation.

A)

-

sin(2x + π)

B)

+

sin(2x - π)

C)

-

cos(2x + π)

D)

+

cos(2x - π)

Answer: B Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 24) Sketch the graph of the function y =

-

sin(2x - π)

Answer:

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

79

25) Match the graph of the sine function to the equation.

A)

-

sin(2x - π)

B)

+

sin(2x + π)

C)

+

cos(2x - π)

D)

-

sin(2x + π)

Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 26) Sketch the graph of the function y =

+

sin(2x + π) over

Answer:

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

80

.

27) Match the graph of the cosine function to the equation.

A)

+

cos(2x - π)

B)

-

sin(2x + π)

C)

+

cos(2x + π)

D)

+

cos(2x - π)

Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 28) Sketch the graph of the function y =

-

cos(2x + π)

Answer:

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

81

29) Match the graph of the sine function to the equation.

A) y =

-

sin(2x + π)

B) y =

+

sin(2x - π)

C) y =

-

cos(2x + π)

D) y =

-

sin(2x - π)

Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 30) The current, in amperes (amps), flowing through an alternating current (AC) circuit at time t is I = 220sin

t>0

What is the maximum current? What is the minimum current? What is the period? What is the phase shift?

Maximum current = ________ Amps Minimum current = ________ Amps Period = ________ seconds Phase shift = ________ seconds Answer: Maximum current = 220 Amps Minimum current = - 220 Amps Period =

seconds

Phase shift = 0.0100 seconds Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

82

31) The current, in amperes (amps), flowing through an alternating current (AC) circuit at time t is I = 220sin

t>0

What is the maximum current? What is the minimum current? What is the period? What is the phase shift?

A) Maximum current = 220 Amps; minimum current = - 220 Amps; period =

π seconds; phase

shift = 100 seconds B) Maximum current = 220 Amps; minimum current = - 220 Amps; period =

seconds; phase

shift = 0.0100 seconds C) Maximum current = 220 Amps; minimum current = - 220 Amps; period =

seconds; phase

shift = 100 seconds D) Maximum current = 220 Amps; no minimum current; period =

seconds; phase shift =

0.0100 seconds Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 32) If a roller coaster at an amusement park is built using the sine curve determined by where x is the distance from the beginning of the roller coaster in feet, then how high does the roller coaster go, and what distance is the roller coaster if it goes through four complete sine cycles?

Height is ________ ft Distance is ________ ft Answer: Height is 110 ft Distance is 5,600 ft Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

83

33) If a roller coaster at an amusement park is built using the sine curve determined by where x is the distance from the beginning of the roller coaster in feet, then how high does the roller coaster go, and what distance is the roller coaster if it goes through five complete sine cycles?

A) Height is 85 ft Distance is 4000 ft B) Height is 4000 ft Distance is 85 ft C) Height is 1800 ft Distance is 2000 ft D) Height is 85 ft Distance is 4000π ft Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02 34) The number of deer on an island varies over time because of the number of deer and amount of available food on the island. If the number of deer is determined by

where

t is in years, then what are the highest and lowest numbers of deer on the island, and how long is the cycle (how long between two different years when the number is the highest)?

Highest number of deer is ________ Lowest number of deer is ________ One cycle is ________ Answer: Highest number of deer is 3,150 Lowest number of deer is 2,250 One cycle is 4 years Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 04, Sec 02

84

35) The number of deer on an island varies over time because of the number of deer and amount of available food on the island. If the number of deer is determined by

where

t is in years, then what are the highest and lowest numbers of deer on the island, and how long is the cycle (how long between two different years when the number is the highest)?

A) Highest number of deer is 1500; lowest number of deer is 1000; one cycle is 8 years B) Highest number of deer is 750; lowest number of deer is 250; one cycle is 8 years C) Highest number of deer is 1500; lowest number of deer is 1000; one cycle is 4 years D) Highest number of deer is 1500; lowest number of deer is 250; one cycle is 4 years Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 04, Sec 02

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Trigonometry, 5e (Young) 85

Chapter 5 5.1

Trigonometric Identities

Trigonometric Identities

1) Use fundamental identities to simplify sin (-x) csc (x).

A) sec2 x B) csc2 x C) 1 D) -1 Answer: D Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 2) Use fundamental identities to simplify cos (-x) csc (-x).

A) sec2 x B) csc2 x C) -cot x D) cot x Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 3) Use fundamental identities to simplify cos (-x) sec (-x) A) sin x x B) C) cos x x D) Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 4) Use fundamental identities to simplify

.

A) cos (x) B) sin (-x) C) cos (-x) D) sin (x) Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 86

(x).

5) Use fundamental identities to simplify

.

A) -1 + csc x B) 1 + cot x C) 1 - cot x D) 1 - csc x Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 6) Use fundamental identities to simplify csc x (1 Answer: sin x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

x).

7) Use fundamental identities to simplify cos x ∙

.

Answer: 1 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 8) Use fundamental identities to simplify

.

Answer: x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 9) Use fundamental identities to simplify

.

Answer: x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

87

10) Verify the trigonometric identity csc (x) - cos (-x) cot x = sin x algebraically.

Answer: csc x - cos (-x) cot x = sin x csc x - cos x ∙ -

= sin x = sin x

= sin x = sin x sin x = sin x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 11) Verify the trigonometric identity (sec (x) - tan x)(csc (x) +1) = cot x algebraically.

Answer: (sec (x) - tan x)(csc (x) +1) = cot x = cot x = cot x = cot x = cot x = cot x = cot x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

88

12) Verify the trigonometric identity Answer:

= sec x + tan x algebraically.

= sec x + tan x = sec x + tan x = sec x + tan x = sec x + tan x

+ +

= sec x + tan x = sec x + tan x

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 13) Verify the trigonometric identity Answer:

+

+

= 1 algebraically.

=1

sin2 x + cos2 x = 1 sin2 x + cos2 x = 1 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 14) Verify the trigonometric identity Answer:

- csc x - sec x algebraically.

- csc x - sec x

sec x + csc x - csc x = sec x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

89

15) Verify the trigonometric identity Answer:

-

-

= 2cot x algebraically.

= 2cot x

cot x + csc x -

= 2cot x

cot x + csc x +

= 2cot x

cot x + csc x + cot x - csc x = 2cot x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 16) Verify the trigonometric identity Answer: 1+

-1+

+

= csc x sec x

= csc x sec x = csc x sec x = csc x sec x

= csc x sec x Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

90

= csc x sec x algebraically.

17) Verify the trigonometric identity

Answer:

= cos x algebraically.

= cos x = cos x = cos x

cos x = cos x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01 18) Determine if = 5 is conditional or is an identity.

A) conditional B) identity Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 19) Determine if 4 A) conditional B) identity Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 01 20) Determine if

= sec x + csc x is conditional or is an identity.

= cos θ - sin θ is conditional or is an identity.

Answer: Identity Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

91

21) Determine if sin θ csc θ θ= Answer: Identity Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 01

θ is conditional or is an identity.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

92

Trigonometry, 5e (Young) Chapter 5 Trigonometric Identities 5.2

Sum and Difference Identities

1) Find the exact value of cos

.

A) B) C) D) Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 2) Find the exact value of cot

.

A) B) C) D) 1 Answer: D Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02

93

3) Find the exact value of cos

.

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 4) Find the exact value of cot

.

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 5) Find the exact value of cos(240°).

A) B) C) D) -1 Answer: A Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 6) Find the exact value of cot(240°).

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02

94

7) Write cos 12x cos 8x + sin 12x sin 8x as a single trigonometric function.

A) sin 4x B) cos 4x C) sin 20x D) cos 20x Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 8) Write cos 8]x cos 3x - sin 8x sin 3x as a single trigonometric function.

A) sin 5x B) cos 5x C) sin 11x D) cos 11x Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 9) Write cos 7x cos 5x + sin 7x sin 5x as a single trigonometric function.

Answer: cos 2x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 10) Write cos 6x cos 5x - sin 6x sin 5x as a single trigonometric function.

Answer: cos 11x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 11) Write sin 7x cos 2x + cos 7x sin 2x as a single trigonometric function.

A) sin 5x B) cos 5x C) sin 9x D) cos 9x Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02

95

12) Write sin 6x cos 3x - cos 6x sin 3x as a single trigonometric function.

A) sin 3x B) cos 3x C) sin 9x D) cos 9x Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 13) Write sin 10x cos 2x + cos 10x sin 2x as a single trigonometric function.

Answer: sin 12x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 14) Write sin 8x cos 4x - cos 8x sin 4x as a single trigonometric function.

Answer: sin 4x Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 15) Choose the trigonometric function that is equivalent to -5 + .

A) -3 + 2sin(A + B) B) -7 - cos(A - B) C) -3 + 2cos(A - B) D) -3 + 2cos(A + B) Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 16) Write -8 + + numerical constants.

Answer: -6 - 2cos(A - B) Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02

+

as a single trigonometric function and

96

17) Write

as a single trigonometric function.

A) tan(9°) B) cot(9°) C) tan(83°) D) cot(83°) Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 18) Write

as a single trigonometric function.

Answer: tan(63°) Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 19) Find the exact value of cos(α - β) if cos α = -

and cos β =

if the terminal side of α lies

in II and the terminal side of β lies in IV. A) B) C) D) Answer: B Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 20) Find the exact value of cos(α + β) if cos α = -

and cos β =

quadrant III and the terminal side of β lies in quadrant I. Answer: Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 97

if the terminal side of α lies in

21) Find the exact value of sin(α - β) if sin α =

and cos β = -

if the terminal side of α lies in

quadrant I and the terminal side of β lies in quadrant III. A) B) C) D) Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 22) Find the exact value of sin(α + β) if sin α =

and cos β =

if the terminal side of α lies in

quadrant II and the terminal side of β lies in quadrant IV. Answer: Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 23) Find the exact value of tan(α - β) if sin α = -

and cos β =

in quadrant IV and the terminal side of β lies in quadrant I. A) B) C) D) Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 98

if the terminal side of α lies

24) Find the exact value of tan (α + β) if sin α = -

and cos β = -

if the terminal side of α lies

in quadrant IV and the terminal side of β lies in quadrant III. Answer: Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 25) Find the exact value of sin (α + β) if sin α = -

and cos β =

if the terminal side of α lies

in quadrant III and the terminal side of β lies in quadrant IV. A) B) C) D) Answer: B Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 26) Find the exact value of tan(α + β) if sin α =

and cos β =

if the terminal side of α lies in

quadrant II and the terminal side of β lies in quadrant IV. Answer: Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 x = cos x is conditional or an identity.

27) Determine if x+ A) conditional B) identity Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 99

28) Determine if

+

= 2tan θ is conditional or an identity.

A) conditional B) identity Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 05, Sec 02 29) Determine if 6 θ+6 θ = 6 is conditional or an identity.

Answer: identity Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02 30) Determine if 5cos θ + 5sin θ = 5 Answer: conditional Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02

is conditional or an identity.

31) Functions. Consider a 22-foot ladder placed against a wall such that the distance from the top of the ladder to the floor is h feet and the angle between the floor and the ladder is θ?. a. Write the height, h, as a function of angle θ. b. If the ladder is pushed toward the wall, increasing the angle θ by 6°, write a new function for the height as the height as a function of θ + 6° and then express in terms of sines and cosines of θ + 6°.

Answer: a) h = 22sin(θ + 6°) b) h = 22sin θ cos 6° + 22cos θ sin 6° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02

100

32) Graph y = cos

sin x + sin

cos x by first rewriting as a sine or cosine of a difference or

sum.

Answer: sin

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02

101

33) Graph y = cos

cos x + sin

sin x by first rewriting as a sine or cosine of a difference or

sum.

Answer: cos

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 05, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

102

Trigonometry, 5e (Young) Chapter 6 Solving Trigonometric Equations 6.1

Inverse Trigonometric Functions

1) Use a calculator to evaluate the expression. Give answer in degrees and round to two decimal places.

(0.0486) Answer: 2.79 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 2) Use a calculator to evaluate the expression. Give answer in degrees and round to two decimal places.

(6.5714) Answer: 8.65 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 3) Use a calculator to evaluate the expression. Give answer in degrees and round to two decimal places.

(-6.2391) Answer: 99.22 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 4) Use a calculator to evaluate the expression. Give answer in degrees and round to two decimal places.

(3.605) Answer: 73.90 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 5) Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

(0.3353) Answer: 1.23 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

103

6) Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

(-6.6853) Answer: 2.99 Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 7) Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

(6.4992) Answer: 1.42 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 8) Use a calculator to evaluate the expression. Give answer in degrees and round to two decimal places.

(-7.2039) Answer: -0.14 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 9) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 10) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

104

11) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 12) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 13) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 14) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

105

15) Evaluate the expression exactly if possible. If not possible, state why.

Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 16) Evaluate the expression exactly. csc Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 17) Evaluate the expression exactly. cot Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 18) The number of hours of daylight in San Diego, California, can be modeled with where t is the day of the year (January 1, t = 1 etc) For what value of t is the number of hours equal to 12.9? If May 31 is the 151st day of the year, what month and day correspond to that value of t? Round to 2 decimal places.

The day of the year is ________.

Answer: 103.61; April 13 to 14 Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

106

19) The horizontal movement of a point that is k kilometers away from an earthquake's fault line

can be estimated with M =

where M is the movement of the point in meters, f is the

total horizontal displacement occurring along the fault line, k is the distance of the point from the fault line, and d is the depth in kilometers of the focal point of the earthquake. If an earthquake produced a displacement, f, of 3.1 meters and the depth of the focal point was 3.7 kilometers, then what is the movement, M , of a point that is 0.82 kilometers from the fault line? Round to 2 decimal places.

Answer: 0.82 m Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 20) A museum patron whose eye level is 6 feet above the floor is studying a painting that is 8 feet in height and mounted on the wall 3 feet above the floor. If the patron is x feet from the wall, θ is the angle that the patron's eye sweeps from the top to the bottom of the painting. Find the measure of the angle θ for x = 17. Round to the nearest degree).

Answer: 26° Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 21) Use a calculator to evaluate the expression.

(-0.9256) A) -67.76° B) 157.76° C) -1.18° D) 67.76° Answer: A Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 22) Use a calculator to evaluate the expression.

(1.2227) A) 50.72° B) 39.28° C) 0.89° D) -50.72° Answer: A Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

107

23) Use a calculator to evaluate the expression.

(-3.5601) A) 106.31° B) -16.31° C) 1.86° D) 73.69° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 24) Use a calculator to evaluate the expression.

(4.0089) A) 14.44° B) 0.25° C) 75.56° D) Not Possible Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 25) Use a calculator to evaluate the expression.

(0.594) A) 0.93 rad B) 0.64 rad C) 36.44 rad D) -0.64 rad Answer: B Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 26) Use a calculator to evaluate the expression.

(-3.9003) A) -75.62 rad B) 2.89 rad C) -1.32 rad D) 1.32 rad Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

108

27) Use a calculator to evaluate the expression.

(4.0644) A) 0.25 rad B) 1.32 rad C) 14.24 rad D) Not Possible Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 28) Use a calculator to evaluate the expression.

(-8.5514) A) 96.72 rad B) -0.12 rad C) 1.69 rad D) Not Possible Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 29) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: B Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

109

30) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 31) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

110

32) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 33) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

111

34) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 35) Evaluate the expression exactly if possible. If not possible, state why.

A) B) C) D) Not Possible Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

112

36) Evaluate the expression exactly. sec A) B) C) D) Not Possible Answer: C Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 37) Evaluate the expression exactly. sin A) B) C) D) Not Possible Answer: B Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 38) The number of hours of daylight in San Diego, California, can be modeled with H(t) =12 + 2.4sin(0.017t - 1.377) where t is the day of the year (January 1, t = 1 etc) For what values of t is the number of hours equal to 10? Round to 2 decimal places.

A) Number of hours is 23.05 B) Number of hours is 231.35 C) Number of hours is 80.01 D) No Solution Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01

113

39) The horizontal movement of a point that is k kilometers away from an earthquake's fault line

can be estimated with M =

where M is the movement of the point in meters, f is the

total horizontal displacement occurring along the fault line, k is the distance of the point from the fault line, and d is the depth in kilometers of the focal point of the earthquake. If an earthquake produced a displacement, f, of 1.7 meters and the depth of the focal point was 2.7 kilometers, then what is the movement, M , of a point that is 4.2 kilometers from the fault line? Round to 2 decimal places.

A) -34.65 km B) 0.21 km C) 0.31 km D) No Solution Answer: C Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 40) A museum patron whose eye level is 5 feet above the floor is studying a painting that is 6 feet in height and mounted on the wall 4 feet above the floor. If the patron is x feet from the wall, θ is the angle that the patron's eye sweeps from the top to the bottom of the painting. Find the measure of the angle θ for x = 12. Round to the nearest degree.

A) 27° B) 0.5° C) 63° D) 5° Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 01 41) Find the exact value of the expression. Give answer in radians in the interval

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

114

.

42) Find the exact value of the expression. Give answer in degrees in the interval (-90°, 180°).

Answer: 45° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 43) Find the exact value of the expression. Give answer in radians in the interval (0, π). () Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 44) Find the exact value of the expression. Give answer in degrees in the interval (0, 180°). () Answer: 120° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 45) Find the exact value of the expression. Give answer in radians in the interval (0, π).

(1) Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 46) Find the exact value of the expression. Give answer in degrees in the interval (0, 180°).

(-1) Answer: 135° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

115

47) Find the exact value of the expression. Give answer in radians in the interval

.

Answer: Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 48) Find the exact value of the expression. Give answer in degrees in the interval (-90°, 180°).

Answer: 60° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 49) Evaluate the expression exactly if possible. If not possible, state why. cos Answer: 1 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 50) Evaluate the expression exactly if possible. If not possible, state why. cos Answer: 1 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01 51) Write an equivalent expression in terms of only the variable u. cos( u) Answer: Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

116

52) Write an equivalent expression in terms of only the variable u. tan( u) Answer: Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 01

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117

Trigonometry, 5e (Young) Chapter 6 Solving Trigonometric Equations 6.2

Solving Trigonometric Equations That Involve Only One Trigonometric Function

1) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. cos θ =Answer:

π,

π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 2) Solve the given trigonometric equation exactly for all reals. cos

=-

Answer: (15 + 40n)π/4, (25 + 40n)π/4 for integer n Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 3) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. cos (2θ) = Answer:

π,

π,

π,

π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

118

4) Solve the given trigonometric equation exactly for all reals. sin

=-

Answer: (14 + 24n)π/3 and (22 + 24n)π/3 for integer n Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 5) Solve the given trigonometric equation exactly for all reals. sec

=2

Answer: (4 + 24n)π/3 and (20 + 24n)π/3 for integer n Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 6) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. csc θ = Answer:

π,

π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 7) Solve the given trigonometric equation exactly over the interval, -2π ≤ θ ≤ 2π. cot (2θ) = π,

Answer:

π,

π,

π,

π,

π,

π,

π

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 8) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

2cos θ = Answer:

π,

π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

119

9) Solve the given trigonometric equation exactly for all reals.

2cos

=

Answer: (2 + 24n)π/3, (22 + 24n)π/3 for integer n Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 10) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. tan (2θ) + =0 Answer:

π,

π,

π,

π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 11) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. cot

+

Answer:

=0 π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 12) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

2sin (2θ) + =0 Answer:

π,

π,

π,

π

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 13) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. θ-3=0 Answer:

π,

π,

π,

π

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

120

14) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. θ-

=0

Answer:

π,

π,

π,

π

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 15) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. θ=0 Answer:

π,

π

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 16) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. θ=0 Answer: 0, π Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 17) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

2 θ - sin θ - 1 = 0 Answer:

π,

π,

π

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 18) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places. csc (2θ) = 3.1407 Answer: 9.28°, 80.72°, 189.28°, 260.72° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

121

19) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places. sec

= 3.8183

Answer: 149.63° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 20) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places. csc

= 1.4374

Answer: 88.17° and 271.83° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 21) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places. tan

= 8.2413

Answer: 166.16° Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 22) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places.

4tan θ - 6 = 0 Answer: 56.31°, 236.31° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 23) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places. sec θ - 3 = 0 Answer: 70.53°, 289.47° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

122

24) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places.

10cos θ =0 Answer: 74.66°, 285.34° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 25) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places.

10 θ + 3cos θ - 1 = 0 Answer: 78.46°, 281.54°, 120.00°, 240.00° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 26) Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places.

10 θ + 15cos θ - 25 = 0 Answer: 158.20°, 338.20°, 45.00°, 225.00° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 27) The monthly sales of soccer balls is approximated by S = 400sin x + 2000 where x is the number of the month (January is x = 1, etc.). During which month do the sales reach $1,653.6?

Answer: July or November Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 28) The monthly sales of soccer balls is approximated by S = 400sin x + 2000 where x is the number of the month (January is x = 1, etc.). During which two months do the sales reach $2,346.4?

Answer: July and November Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

123

29) The number of deer on an island is given by D = 300 + 100sin x where x is the number of years since 2000. During what year is it the first time after 2000 that the number of deer reaches 4?

Answer: 2003 Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 30) Solve the given trigonometric equation exactly over the interval, 0 ≤? θ? ≤? 2π? sin θ = A)

π,

π

B)

π,

π

C)

π,

π

D)

π,

π

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

124

31) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. cos2θ = A)

π,

π,

π,

π

B)

π,

π,

π,

C)

π,

π,

π,

π

D)

π,

π,

π,

π

π

Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 32) Solve the given trigonometric equation exactly for all reals. sin

=

A)

π and

B)

π and

π for integer n

C)

π and

π for integer n

D)

π and

π for integer n

π for integer n

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

125

33) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. cscθ = A)

π,

π

B)

π,

π

C)

π,

π

D)

π,

π

Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 34) Solve the given trigonometric equation exactly for all reals.

2sin

=

A)

π and

π for integer n

B)

π and

π for integer n

C)

π and

π for integer n

D)

π and

π for integer n

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

126

35) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. cot 2θ -

=0

A)

π,

π,

π,

π

B)

π,

π,

π,

π

C)

π,

π,

π,

π

D)

π,

π,

π,

π

Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 36) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. tan

-

A)

π

B)

π

C)

π,

=0

π

D) none of the above Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

127

37) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

2cos 2θ +

=0

A)

π,

π,

π,

π

B)

π,

π,

π,

π

C)

π,

π,

π,

π

D) none of the above Answer: C Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 38) Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π. θ + cscθ - 2 = 0 A)

π,

π,

π

B)

π,

π,

π

C)

π,

π,

π

D)

π,

π,

π

Answer: D Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 39) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places. cos 2θ = 0.4963 A) 30.12°, 149.88°, 210.12°, 329.88° B) 30.12°, 149.88°, 59.88°, 59.88° C) 59.88°, 59.88°, 239.88°, 239.88° D) 210.12°, 329.88°, 59.88°, 59.88° Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 128

40) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places. sec

= 1.3751

A) 136.65° B) 43.35° C) 86.70° D) no solution Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 41) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places. sin

= 0.2178

A) 25.16° B) 12.58°, 167.42° C) 192.58° D) no solution Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 42) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places. tan

= -9.1864

A) 167.57° B) 192.43° C) 83.79° D) no solution Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

129

43) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places. tanθ + 6 = 0 A) 99.46°, 279.46° B) 99.46°, 80.54° C) 279.46°, 260.54° D) 80.54°, 260.54° Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 44) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

9 secθ - 10 = 0 A) 25.84°, 334.16° B) 25.84°, 154.16° C) 334.16°, 205.84° D) 154.16°, 205.84° Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 45) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

6 cosθ =0 A) 38.58°, 141.42° B) 321.42°, 218.58° C) 38.58°, 321.42° D) 141.42°, 218.58° Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

130

46) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

15 θ - 7 cosθ - 2 = 0 A) 48.19°, 311.81°, 101.54°, 258.46° B) 48.19°, 131.81°, 101.54°, 78.46° C) 311.81°, 131.81°, 258.46°, 281.54° D) 131.81°, 228.19°, 78.46°, 281.54° Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 47) Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

15 θ - 18 cotθ - 24 = 0 A) 26.57°, 206.57°, 128.66°, 308.66° B) 26.57°, 153.43°, 128.66°, 51.34° C) 206.57°, 333.43°, 308.66°, 231.34° D) 153.43°, 333.43°, 51.34°, 231.34° Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 48) The monthly sales of soccer balls is approximated by S = 400sin x + 2000 where x is the number of the month (January is x = 1, etc.). During which two months do the sales reach 1800?

A) July and November B) July and October C) May and November D) July and September Answer: A Diff: 3 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02

131

49) Deer Population. The number of deer on an island is given by

where

x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 30.

Answer: 2009 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 50) Calculus. In Calculus, the term "critical numbers" refers to values for x, where a graph may have a maximum or minimum. To find the critical numbers of the equation solve the equation for all values of x.

Answer:

+

n, where n is an integer

Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02 51) Angle of Elevation. If a 8-foot lamppost makes a 10-foot shadow on the sidewalk, find its angle of elevation to the sun.

A) 53° B) 37° C) 51° D) 39° Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 06, Sec 02 52) Angle of Elevation. If a 7-foot lamppost makes a 11-foot shadow on the sidewalk, find its angle of elevation to the sun. Give the answer in degrees.

Answer: 32° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 06, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

132

Trigonometry, 5e (Young) Chapter 7 Applications of Trigonometry: Triangles and Vectors 7.1

Oblique Triangles and the Law of Sines

1) Classify the triangle as AAS, ASA, SSA, SAS, or SSS given the following information.

a, a, b Answer: AAS Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 2) Classify the triangle as AAS, ASA, SSA, SAS, or SSS given the following information.

a, c, β Answer: SSA Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01

133

3) Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits.

c = 244 in., γ = 45.8°, α = 37° Answer: β = 97.2°, a = 205 in., b = 338 in.

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 4) Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits.

a = 183 yd., β = 71.6°, γ = 37.8° Answer: α = 70.6°, b = 184 yd., c = 119 yd.

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 5) Solve the given triangle. Round angles to one decimal place and side measure to 3 significant figures.

c = 73 m., a = 70 m., γ = 65° Answer: α = 60.3°, β = 54.7°, b = 65.7 m.

Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 134

6) Solve the given triangle. Round angles to one decimal place and side measures to 3 significant figures.

c = 83 m., a = 107.5 m., γ = 44.5° Answer: Case one: = 65.2°, Case two:

= 114.8°,

= 20.7°,

= 70.2963541°, = 41.9 m.

Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 7) Solve the given triangle.

c = 7.0 cm., γ = 47.4°, α = 49.6° A) β = 83°, a = 7.2 cm., b = 9.4 cm.

B) β = 83°, a = 9.4 cm., b = 7.2 cm.

C) β = 83°, a = 6.8 cm., b = 9.1 cm.

D) β = 83°, a = 5.2 cm., b = 5.4 cm.

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01

135

= 112 m.

8) Solve the given triangle.

a = 57.0 cm., β = 60.0°, γ = 30.4° A) α = 89.6°, b = 49.4 cm., c = 28.8 cm.

B) α = 89.6°, b = 28.8 cm., c = 49.4 cm.

C) α = 89.6°, b = 65.8 cm., c = 33.3 cm.

D) α = 89.6°, b = 112.6 cm., c = 57.0 cm.

Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01 9) Solve the given triangle.

a = 230.0 ft., b = 42.5 ft., α = 74.5° A) β = 10.3°, γ = 95.2°, c = 237.7 ft.

B) β = 95.2°, γ = 10.3°, c = 237.7 ft.

C) β = 10.3°, γ = 95.2°, c = 222.6 ft.

D) no solution Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01

136

10) Solve the given triangle.

a = 103.0 m., b = 110.0 m., α = 35.5° A) Case one: = 38.3°, = 106.2°, Case two: B) Case one: Case two:

= 141.7°,

= 2.8°,

= 38.3°, = 2.8°,

= 8.7 m.

= 106.2°,

= 141.7°,

= 170.4 m. = 170.4 m.

= 8.7 m.

C) β = 38.3°, γ = 106.2°, c = 170.4 m. and no ambiguous case D) no solution Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01 11) A hot air balloon is sighted at the same time by two friends who are 2.5 miles apart on the same side of the balloon. The angles of elevation from the two friends are 14° and 20°. How high is the balloon? Round to one decimal place.

Answer: 2.0 miles Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 12) A tracking station has two telescopes that are 2.3 miles apart. The telescopes can lock onto a rocket after it is launched and record the angles of elevation to the rocket. If the angles of elevation from telescope A and B are 20° and 63.5°, respectively, then how far is the rocket from telescope B? Round to one decimal place.

Answer: 1.1 miles Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01

137

13) An engineer wants to construct a bridge across a fast moving river. Using a straight line segment between two points that are 180 feet apart along his side of the river, he measures the angles formed when sighting the point on the other side where he wants to have the bridge end. If the angles formed at points A and B are 44° and 66°, respectively, how far is it from point A to the point on the other side of the river? Round to one decimal place.

Answer: 175 feet Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 01 14) A hot air balloon is sighted at the same time by two friends who are 1.9 miles apart on the same side of the balloon. The angles of elevation from the two friends are 12.5° and 19°. How high is the balloon?

A) 1.2 miles B) 0.1 mile C) 0.3 mile D) no solution Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01 15) A tracking station has two telescopes that are 3 miles apart. The telescopes can lock onto a rocket after it is launched and record the angles of elevation to the rocket. If the angles of elevation from telescope A and B are 34.5° and 66°, respectively, then how far is the rocket from telescope A? A) 1.7 miles B) 3.3 miles C) 5.2 miles D) no solution Answer: C Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01

138

16) An engineer wants to construct a bridge across a fast moving river. Using a straight line segment between two points that are 185 feet apart along his side of the river, he measures the angles formed when sighting the point on the other side where he wants to have the bridge end. If the angles formed at points A and B are 57° and 39°, respectively, how far is it from point A to the point on the other side of the river?

A) 156.0 feet B) 117.1 feet C) 292.4 feet D) no solution Answer: B Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

139

Trigonometry, 5e (Young) Chapter 7 Applications of Trigonometry: Triangles and Vectors 7.2

The Law of Cosines

1) Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits.

c = 210 yd., a = 205 yd., b = 176 yd.

Answer: γ = 66.4°, α = 63.4, β = 50.2° Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02 2) Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits.

c = 46 ft., α = 70.6, b = 24.0 ft.

Answer: γ = 78.6°, β = 30.8°, a = 44.3 ft.

Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02

140

3) Solve the given triangle.

a = 83 in., b = 99.7 in., c = 95.7 in.

A) α = 50.2°, β = 67.4°, γ = 62.4° B) α = 62.4°, β = 50.2°, γ = 67.4° C) α = 67.4°, β = 62.4°, γ = 50.2° D) no solution Answer: A Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02 4) Solve the given triangle.

a = 89 in., β = 52.2, c = 68.5 in.

A) α = 78.8°, γ = 49.0°, b = 71.7 in.

B) α = 49.0°, γ = 78.8°, b = 67.9 in.

C) α = 78.8°, γ = 49.0°, b = 101 in.

D) no solution Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 02 5) A plane flew due north at 460 mph for 3.5 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 112° clockwise from due north for 3.5 hours. If, at the end of the 3.5 hours, the two planes were 2,500 miles apart, how fast was the second plane traveling?

Answer: 397 mph Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02

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6) A 21 foot slide leaning against the bottom of a building's window makes a 54° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 37°. How tall is the window? Round to the nearest integer.

Answer: 10 feet Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02 7) Peg and Meg live five miles apart. The school that they attend lies on a street that makes a 38° angle with the street connecting their houses when measured from Peg's house. The street connecting Meg's house and the school makes a 44° angle with the street connecting them. How far is it from Peg's house to the school?

Answer: 3.5 miles Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02 8) An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 20° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 27°, then how long is the slide?

Answer: 37 feet Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02 9) A plane flew due north at 320 mph for 3 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 126° clockwise from due north for 3 hours. If, at the end of the 3 hours, the two planes were 2300 miles apart, how fast was the second plane traveling?

A) nan mph B) 1590 mph C) 530 mph D) no solution Answer: C Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 02

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10) A 67 foot slide leaning against the bottom of a building's window makes a 51° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 40°. How tall is the window?

A) 81 feet B) 20 feet C) 273 feet D) no solution Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 02 11) Peg and Meg live three miles apart. The school that they attend lies on a street that makes a 27° angle with the street connecting their houses when measured from Peg's house. The street connecting Meg's house and the school makes a 45° angle with the street connecting them. How far is it from Peg's house to the school?

A) 2.2 miles B) 1.4 miles C) 4.0 miles D) no solution Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 02 12) An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 38° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 48°, then how long is the slide?

A) 19 feet B) 21 feet C) 7 feet D) no solution Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 07, Sec 02

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13) Decide whether the Law of Cosines is needed to solve this triangle.

Given: sides a, b, and c A) Do NOT need Law of Cosines B) Do need Law of Cosines Answer: B Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 07, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Trigonometry, 5e (Young) 144

Chapter 8 8.1

Complex Numbers, Polar Coordinates, and Parametric Equations

Complex Numbers

1) Simplify.

Answer: 1 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 2) Simplify.

Answer: 12i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 3) Perform the operation, simplify, and express in standard form.

(-5 + 5i)(-3 - 13i) Answer: 80 + 50i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 4) Perform the operation, simplify, and express in standard form.

Answer: Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 5) Perform the operation, simplify, and express in standard form.

Answer: Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01

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6) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

8 - 14 -3 Answer: -32i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 7) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

(9 - 8i)(7 + 4i) Answer: 95 - 20i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 8) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

Answer: 70 + 140i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 9) Simplify.

A) -i B) 1 C) -1 D) no solution Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 10) Simplify.

A) 17 B) -17i C) 17i D) no solution Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 146

11) Perform the operation, simplify, and express in standard form.

(8 - 3i)(9 + 11i) A) 105 + 61i B) 39 + 61i C) 61 - 39i D) 61 + 105i Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 12) Perform the operation, simplify, and express in standard form.

A) B) C) D) Answer: C Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 13) Perform the operation, simplify, and express in standard form.

A) B) C) D) Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 147

14) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

-3 - 15 - 11 A) -120i B) -60i C) 12i D) 72i Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 15) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

12 - 14 + 20 A) 14i B) 210i C) -66i D) 130i Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 16) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

(-9 + 4i)(-1 - 8i) A) -23 + 68i B) 41 + 68i C) -23 + 76i D) -44 + 76i Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 17) Write the negative radicals in terms of imaginary numbers and then perform the operations and simplify.

A) 36 - 142i B) -12 - 142i C) -36 + 156i D) 12 - 156i Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 148

18) Simplify and express in standard form.

A) 5 B) 5 - 12i C) 5 + 12i D) 13 - 12i Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 01 19) Simplify and express in standard form.

Answer: -234 - 415i Diff: 3 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01 20) Write the complex conjugate of 2 - 15i Answer: 2 + 15i Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 01

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Trigonometry, 5e (Young) Chapter 8 Complex Numbers, Polar Coordinates, and Parametric Equations 8.2

Polar (Trigonometric) Form of Complex Numbers

1) Graph the complex number.

-4 + 3i

Answer:

Diff: 1 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 2) Express the complex number in polar form.

3 + 3i Answer: 3 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02

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3) Express the complex number in polar form. + i Answer: Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 4) Express the complex number in polar form.

-7 + 7 i Answer: 14 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 5) Express the complex number in polar form.

6 + 6i Answer: 12 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 6) Express the complex number in polar form.

-2 + 0i Answer: 2(cos π + i sin π) Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 7) Use a calculator to express the complex number in polar form. Round angle to one decimal place and in degrees.

-8 - 6i Answer: 10(cos 216.9° + i sin 216.9°) Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02

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8) Use a calculator to express the complex number in polar form. Round angle and length to one decimal place and in degrees.

3 + 7i Answer: (cos 66.8° + i sin 66.8°) or 7.6(cos 66.8° + i sin 66.8°) Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 9) Use a calculator to express the complex number in polar form. Round angle to one decimal place and in degrees.

-24k + 7ki where k > 0 Answer: 25k(cos 163.7° + i sin 163.7°) Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 10) Express the complex number in rectangular form.

10 Answer: -5 -5 i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 11) Express the complex number in rectangular form.

6(cos 300° + i sin 300°) Answer: 3 - 3 i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 12) Express the complex number in rectangular form.

10(cos 30° + i sin 30°) Answer: 5 + 5i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02

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13) Use a calculator to express the complex number in rectangular form. Round to four decimal places.

4(cos 154° + i sin 154°) Answer: -3.5952 + 1.7535i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 14) Use a calculator to express the complex number in rectangular form. Round to four decimal places.

-15 Answer: 9.3523 + 11.7275i Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 15) Force A, at 20 pounds, and force B, at 200 pounds, make an angle of 145° with each other.

Represent their respective vectors as complex numbers written in trigonometric form and solve for the resultant force to one decimal place.

Answer: Trigonometric form: 20(cos 0° + i sin 0°) + 200(cos 145° + i sin 145°) or Resultant force: 184.0 pounds Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02 16) Force A, at 140 pounds, and force B, at 35 pounds, make an angle of 150° with each other.

Represent their respective vectors as complex numbers written in trigonometric form and solve for the resultant angle to one decimal place.

Answer: Trigonometric form: 140(cos 0° + i sin 0°) + 35(cos 150° + i sin 150°) or Resultant angle: 9.1° Diff: 4 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02

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17) Select the complex number that matches the graph.

A) 5 - 4i B) 4 - 5i C) -5 + 4i D) -4 + 5i Answer: C Diff: 1 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 18) Express the complex number in polar form.

-7 + 7i A) 7 B) 7 C) 7 D) 7 Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02

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19) Express the complex number in polar form. + i A) B) C) D) 2 Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 20) Express the complex number in polar form.

5+5 A) 10 B) 10 C) 5 D) 10 Answer: B Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02

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21) Express the complex number in polar form.

5 + 5i A) 10 B) 10 C) 10 D) 10 Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 22) Express the complex number in polar form.

5 + 0i A) 5(cos 0 + i sin 0) B) 5(cos π + i sin π) C) -5(cos 0 + i sin 0) D) no solution Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 23) Use a calculator to express the complex number in polar form.

8 - 6i A) 10(cos 323.1° + i sin 323.1°) B) 10(cos 143.1° + i sin 143.1°) C) 10(cos 216.9° + i sin 216.9°) D) 10(cos 36.9° + i sin 36.9°) Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02

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24) Use a calculator to express the complex number in polar form.

4 + 5i A) (cos 308.7° + i sin 308.7°) B) (cos 231.3° + i sin 231.3°) C) (cos 128.7° + i sin 128.7°) D) (cos 51.3° + i sin 51.3°) Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 25) Use a calculator to express the complex number in polar form.

12d + 5di A) 13d(cos 22.6° + i sin 22.6°) B) 13d(cos 202.6° + i sin 202.6°) C) 13d(cos 157.4° + i sin 157.4°) D) 13d(cos 337.4° + i sin 337.4°) Answer: A Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 26) Express the complex number in rectangular form.

16 A) -8 - 8i B) 8 +8 i C) -8 -8 i D) 8 -8 i Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 27) Express the complex number in rectangular form.

4(cos 120° + i sin 120°) A) -2 - 3 i B) 2 - 2 i C) -2 + 2 i D) -2 - 3i Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 157

28) Express the complex number in rectangular form.

14(cos 30° + i sin 30°) A) 7 - 7i B) -7 - 7i C) 7 + 7 i D) 7 + 7i Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 29) Use a calculator to express the complex number in rectangular form.

9(cos 236° + i sin 236°) A) -5.0327 + 7.4613i B) 5.0327 + 7.4613i C) -5.0327 - 7.4613i D) 5.0327 - 7.4613i Answer: C Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 30) Use a calculator to express the complex number in rectangular form.

-16 A) -13.4601 - 8.6503i B) -13.4601 + 8.6503i C) 13.4601 + 8.6503i D) 13.4601 - 8.6503i Answer: D Diff: 2 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02

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31) Force A, at 380 pounds, and force B, at 770 pounds, make an angle of 135° with each other.

Represent their respective vectors as complex numbers written in trigonometric form and solve for the resultant force.

A) Trigonometric form: 380(cos 0° + i sin 0°) + 770(cos 135° + i sin 135°) Resultant force: 568.8 pounds B) Trigonometric form: 770(cos 0° + i sin 0°) + 380(cos 135° + i sin 135°) Resultant force: 568.8 pounds C) Trigonometric form: 380(cos 135° + i sin 135°) + 770(cos 135° + i sin 135°) Resultant force: 568.8 pounds D) Trigonometric form: 380(cos 135° + i sin 135°) + 770(cos 0° + i sin 0°) Resultant force: 568.8 pounds Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 32) Force A, at 300 pounds, and force B, at 770 pounds, make an angle of 80° with each other.

Represent their respective vectors as complex numbers written in trigonometric form and solve for the resultant angle.

A) Trigonometric form: 300(cos 0° + i sin 0°) + 770(cos 80° + i sin 80°) or 770(cos 0° + i sin 0°) + 300(cos 80° + i sin 80°) Resultant angle: 60.2° B) Trigonometric form: 300(cos 0° + i sin 0°) + 770(cos 80° + i sin 80°) Resultant angle: 60.2° C) Trigonometric form: 300(cos 80° + i sin 80°) + 770(cos 80° + i sin 80°) Resultant angle: 60.2° D) Trigonometric form: 300(cos 0° + i sin 0°) + 770(cos 80° + i sin 80°) or 770(cos 0° + i sin 0°) + 300(cos 80° + i sin 80°) Resultant angle: 119.8° Answer: A Diff: 4 Var: 1 Question Type: Multiple Choice Chapter/Section: Ch 08, Sec 02 33) Express the complex number in rectangular form.

18(cos π + i sin π) Answer: 18 Diff: 2 Var: 1 Question Type: Short Answer Chapter/Section: Ch 08, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

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© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

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