Math Test: Trigonometric Equations

Part A (20pts): Answer in the spaces provided.

1. sin 225o = ______(1)

2. cos 330o = ______(2)

3. sin245o + cos245o = ______(3)

4. csc 30o = ______(4)

5. tan 60o = (do NOT us decimal) ______(5)

6. Express 330o in radians ______(6)

7. Express 7π/6 in degrees ______(7)

8. On the unit circle, what point would you be at o if you performed the following rotation: R150 (1,0) ______(8)

3 9. Solve: sin x  ______(9) 2

10. What is the arc length of the indicated angle ? ______(10)

Part B (8pts):

12. Convert to Radians: a) 195o b) 1080o

13. Convert to Degrees: a) 9π/5 b) 9.42 Part C(30pts):

14. Solve for x (all possible angles): (5pts each)

a) cos2x + 2 cos x – 3 = 0 b) 2cos x  3  0

c) 5 sin x + 1 = 0 d) sin x = 1/2

15. A rubber ball is dropped from a height of 10m and takes 1 second to hit the ground. After 1 more second, the ball bounces back up to a height of 10m. This pattern repeats until the experiment is stopped. (10pts)

a) Use a cosine equation to describe this periodic motion with y representing height and x representing time.

b) Use the equation to determine all the times when the ball is 9m above the ground.

Part D (18pts): Simplify: sin 450 2 a) b) cos3300 1 2sin 600

2sin1200 c) 6sin 300  4cos 450

Part E (24pts): Prove the following identities: a) 4 cot2x csc x tan x = 4 cot x b) 2 cos x + 2 tan2x cos x = 2 sec x

cos 2 x c) sin x   csc x sin x