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Pre Calculus Unit 9 Review 1 This test is cumulative over ALL trig taught so far!!! Simplify the following trigonometric expressions. 1. sinx cos2x - sinx 2. sinA + cot A cos A 3. Factor Completely. 5. tan2 x – 25 Simplify 7. sin x cot x 1 cos x 4. 6. cot2(A) - cot(A) - 12 cos x 1 sin x 1 sin x cos x 8. sec2 x 1 sin 2 x 1 1 ( cos x) sin x cos x Prove the 4 identities shown below. Remember to show all steps, completely and neatly. If your work can not be read or followed, it would be counted wrong. (Separate Paper!) Show work going down. 9. 11. sec2 A 1 sin 2 A sec2 A sin x csc x cot x 1 cos x 10. 4 4 8 csc 2 x 1 cos x 1 cos x 12. tan x + cot x = sec x csc x Solve the following problems using the appropriate sum and difference identities. SHOW ALL WORK! 4 4 and Cos , find cos ( ). 7 13 4 4 14. Given Sin = and is in Quad II and Cos with in Quad III. Find sin ( ). 7 13 7 15. Find cos 255 16. Find sin 12 13. Angles and are both in the QI. Sin = Pre Calculus Unit 9 Review 1 This test is cumulative over ALL trig taught so far!!! Simplify the following trigonometric expressions. 1. sinx cos2x - sinx 2. sinA + cot A cos A 3. Factor Completely. 5. tan2 x – 25 Simplify 7. sin x cot x 1 cos x 4. 6. cot2(A) - cot(A) - 12 cos x 1 sin x 1 sin x cos x 8. sec2 x 1 sin 2 x 1 1 ( cos x) sin x cos x Prove the 4 identities shown below. Remember to show all steps, completely and neatly. If your work can not be read or followed, it would be counted wrong. (Separate Paper!) Show work going down. 9. 11. sec2 A 1 sin 2 A sec2 A sin x csc x cot x 1 cos x 10. 4 4 8 csc 2 x 1 cos x 1 cos x 12. tan x + cot x = sec x csc x Solve the following problems using the appropriate sum and difference identities. SHOW ALL WORK! 4 4 and Cos , find cos ( ). 7 13 4 4 14. Given Sin = and is in Quad II and Cos with in Quad III. Find sin ( ). 7 13 7 15. Find cos 255 16. Find sin 12 13. Angles and are both in the QI. Sin = Solve the following trig equations for the indicated domain. 17. 2sinA – 1 = 0 ; for all angles in degree measure 18. 2sin2u – sin u - 1 = 0 ; for [0, 360] 3 = 0; for all angles in radian measure. 3 20. 4 cos2 - 1 = 0 for 0 180 2 21. 2cos 3cos 1 for 0 360 1 Review: 22. Evaluate Arccos ( ) in degrees. 2 2 23. The period of the function f(x) = 4cos (x+2) is: 3 7 24. Find the exact value for sin . 4 19. tan A – 25. Find the asymptotes for the following two equations: a. b. y 3cot 3( 40) y 5 tan 2( x ) 3 3 ) 3 y 3cos 2( 45) 26. Find all the angles in radian measure for Arc tan( Graph two full cycles of the following graphs: 28. y 2 csc 6 ( x 4) 29. y 27. 1 cot 2( x ) 4 4 Solve the following trig equations for the indicated domain. 17. 2sinA – 1 = 0 ; for all angles in degree measure 18. 2sin2u – sin u - 1 = 0 ; for [0, 360] 3 = 0; for all angles in radian measure. 3 20. 4 cos2 - 1 = 0 for 0 180 2 21. 2cos 3cos 1 for 0 360 1 Review: 22. Evaluate Arccos ( ) in degrees. 2 2 23. The period of the function f(x) = 4cos (x+2) is: 3 7 24. Find the exact value for sin . 4 19. tan A – 25. Find the asymptotes for the following two equations: b. b. y 3cot 3( 40) y 5 tan 2( x ) 3 3 ) 3 y 3cos 2( 45) 26. Find all the angles in radian measure for Arc tan( Graph two full cycles of the following graphs: 28. y 2 csc 6 ( x 4) 29. y 27. 1 cot 2( x ) 4 4