Mathematics 17 Fifth Long Exam

08 October 2007

This exam is good for 1 hour and 15 minutes only. Use black or blue ballpen â&#x20AC;&#x201C; no pencils. For computations, show all your solutions and BOX your final answers. I. Write TRUE if the statement is true. Otherwise, write FALSE.

(1 pt each)

1. The Arcsine and Arccosine functions are periodic. 2. For all real values of x, tan (Arc tan x) = x. 3. There is no triangle having sides of length 3, 4, and 7 cm. 4. The graph of the function y = Arc cot x has no x-intercept. 5. The principal argument of Î¸ of any complex number is unique. II. Do as indicated. 1. Determine the number of triangles formed given that Îą = 60o, a = 9, b = 10.

(2 pts)

2. Evaluate:  2 â&#x2C6;&#x2019;  +  â&#x2C6;&#x161;2.

(4 pts)

3. Find the exact value of cot( csc-1(sec 210o) â&#x20AC;&#x201C; 2100).

(4 pts)



4. Simplify:

â&#x2C6;&#x161; . â&#x2C6;&#x161;â&#x2C6;&#x161;

.

(4 pts)

III. Find the solution set of the following.

(4 pts each) 

1.  â&#x2C6;&#x161; â&#x2C6;&#x2019;  â&#x2C6;&#x161;1 â&#x2C6;&#x2019;  =    "

"

2. 3  +   + 2#   +   = 3, 0 < x < 2Ď&#x20AC; 3. 4cos4x â&#x20AC;&#x201C; 3cos2x + 2 = 0, 0 < x < 2Ď&#x20AC; 4.   â&#x2C6;&#x2019; â&#x2C6;&#x161;6 â&#x2C6;&#x2019; â&#x2C6;&#x161;2#=0 IV. Word Problems.

(5 pts each)

1. The M17 U5 class in a childrenâ&#x20AC;&#x2122;s park observed that a 28-feet slide makes an angle of 30o with the ground. Its top is reached by the ladder inclined 45o to the ground. Find the length of the ladder and the distance of the top of the slide from the ground. 2. A lamp post is 100 feet away from the Math building. From a point on the top of the building, the angle of depression of the top of the post is 30o, while the angle of depression of its base is 600. Find the height of the lamp post. 3. The M17 W5 class on a cruise ship sailed due east from a point A to a point B for â&#x2C6;&#x161;6 mi. Then it turned in the direction N 75o W and sailed to a point C which is 2 mi away from point B. If the ship is found to be â&#x2C6;&#x161;3 - 1 mi away from A, what is the bearing of the ship from A? V. BONUS: Four suspects of a crime made the following statements to the police: *Dora: Boots did it. *Boots: Swiper did it. *Diego: I did not do it. *Swiper: Boots lied when he said that I did it. (a) Given that exactly one of the four statements is true, determine who did it. (a) Given that exactly one of the four statements is false, determine who did it. TOTAL: 50 POINTS â&#x20AC;&#x153;The primary question is not â&#x20AC;&#x2DC;What do we know?â&#x20AC;&#x2122; but â&#x20AC;&#x2DC;How do we know itâ&#x20AC;&#x2122; â&#x20AC;? -Aristotle rtrelator0708

[0708a] math 17 5th le