1 Review for Test IV MAT146 FALL 2011 1. If 4,052sin and 12,13 2cos, find a. sin( ) b. cos( ) 2. Prove that sin( ) sinxx 3. Verify the identity: sin42cos2sin2. 4. Find sin2x and cos2x if 45cosx  and the angle is in the first quadrant. 5. Find all solutions in [0,2 ) that satisfy the following equations: a. 2cos2 1 0x b. 23sin sinxx c. 29sin 12sin 4 0xx   d. cos2 0x  6. Determine if the following is an identity: 2cot sin sec cos 1x x x x. 7. Use an appropriate identity to simplify the following statements: a. 2sin cos33          b. sin cos cos sin4 3 4 3                         8. Solve: 22cos 5cos 2 0xx  . 9. Verify the identity: 1211tan(sin )416 ( 1)xxx. 10. Solve: cos( ) cos( ) 144xx   . (No solutions posted for these)2 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. a. b. c. d. e. ____ 2. Which of the following is equivalent to the given expression? a. b. c. d. e. ____ 3. Which of the following is a solution to the given equation? a. b. c. d. e.3 ____ 4. Solve the multiple-angle equation. a. b. c. d. e. ____ 5. Write the given expression as the sine of an angle. a. b. c. d. e. ____ 6. Find the exact value of the given expression. a. b. c. d. e.4 ____ 7. Simplify the given expression algebraically. a. b. c. d. 1 e. ____ 8. Find the exact solutions of the given equation in the interval . a. b. c. d. e. ____ 9. Use the figure below to find the exact value of the given trigonometric expression. 15 36 (figure not necessarily to scale) a. c. b. d. e. 10. Verify the identity shown below. (Solutions below)5 Answer Section MULTIPLE CHOICE 1. ANS: D 2. ANS: D 3. ANS: E 4. ANS: B 5. ANS: A 6. ANS: C 7. ANS: E 8. ANS: D 9. ANS: A 10.