Mathematics 17 Fourth Long Exam

28 September 2007

This exam is good for 1 hour and 15 minutes only. Use black or blue ballpen â&#x20AC;&#x201C; no pencils. No cellphones and calculators. For calculations, show all your necessary solutions and box your final answers. God bless! I. TRUE or FALSE

(1 pt each)

1. The equation 9 cos2 Î¸ â&#x20AC;&#x201C; 16 = 0 has one real solution. 2. The graph of y = cos(sin x) is symmetric with respect to the y-axis. 3. sin 5 is negative. 4. The graph of f(x) = cot x has no y-intercepts.

5. If Î¸ Ďľ â&#x201E;? and P(Î¸) = (x, y), then P (Î¸, -Ď&#x20AC;) = (-y, -x).

(2 pts each)



1. For any Î¸ Ďľ â&#x201E;?, tan  â&#x2C6;&#x2019; is equal A. - tan Î¸

B. tan Î¸

C. cot Î¸

D. â&#x20AC;&#x201C;cot Î¸

2. The distance between the point Q (cos 5, sin 5) and the origin is A. 5

C. 1

B. 5â&#x2C6;&#x161;2

D. not possible to determine

3. A central angle subtends an arc length of 12 in a circle of diameter equal to 4. What is the measure of the central angle? 

B.  Â°

A. 6o

C. 



Â° 

D. (12Ď&#x20AC;)o

4. If the point with the coordinates (-2, 1) lies on the terminal side of the angle in standard position with measure Îą, then what is the value of sec Îą? A. â&#x2C6;&#x2019;

â&#x2C6;&#x161; 

B.

â&#x2C6;&#x161; 

C.

5. Two coterminal angles in radian measure differ by

â&#x2C6;&#x161; 

A. multiples of Ď&#x20AC;

C. odd multiples of 2Ď&#x20AC;

B. odd multiples of Ď&#x20AC;

D. even multiples of Ď&#x20AC;

D. â&#x2C6;&#x2019;5

III. Do as indicated. A. Find the exact value of the following: 1. sin 105o cos(2(262.5o)) â&#x20AC;&#x201C; sin(2(262.5o)) cos 105o 2. cot 75o + tan15o 3.

(3 pts each)

B. Given that  = â&#x2C6;&#x2019; 1.  

2. sin 

 

+ 

3. cot 2Î˛

C. Given the equation

 , 



P(Îą) in QIV; and  = â&#x2C6;&#x2019;  , Ď&#x20AC; < Î˛ <

 . 

Find:

(3 pts each)



= â&#x2C6;&#x2019;3"#  â&#x2C6;&#x2019; 5 + 3.

1. Sketch the graph on the interval 10 < x < 4Ď&#x20AC; +10. Label important points.

(3 pts)

2. Give the period, maximum, minimum, and amplitude of the function.

(2 pts)

3. What are the zeros of the function?

(2 pts)

4. Give the displacement of the graph.

(2 pts)

D. Prove the following identities:

(4 pts each)

1. (1 + sin x + cos x)2 = 2(1 + sin x)(1 + cos x) 2. E. BONUS: Find the value of Îą + Î˛, where 00 < Îą, Î˛ < 180o, if 3 "# + "# = % 2 and 1 & + & = % 2

TOTAL : 50 POINTS â&#x20AC;&#x153;Intelligence plus character that is the goal of true education.â&#x20AC;? -Martin Luther King, Jr. rtrelator0708

Math 17 - LE 4

&amp; WY/s &amp; dKd&gt;WK/Ed^