Math Chapter 5 Test Review 1 Answers

Honors Pre-Calculus Chapter 5 Test Review #1 Evaluate (exact answers). 1. 5  sin   arccos  6 2 1.)_________________ 2. 3  cos   arctan  7  2.)_________________ 3. 5 1 sin arccos  13  2 3.)_________________ Solve the following trig equations for [0,2 ) . 4. cot x cos 2 x  2 cot x 4.)_________________ 5. cos 4 x  7 cos 2 x  8 5.)_________________ 6. sin 4 x  sin 2 x  0 6.)_________________ Name the trigonometric function that is equivalent to the expression. 1 1 7. 8. 9. 1 tan 2 x tan x sin x 7.)___________________ 8.)___________________ 9.)___________________ 10.   cos  x   2 11. tan x  10.)__________________ 11.)__________________ Use the given values to evaluate (if possible) the remaining trigonometric functions of the angle. 2 13 2 2 12.)__________________   12. 13. tan   , sec  csc     3, sin   3 3 2 3   13.)__________________ Simplify. 14. sec 2 x  1 sec x  1 15. sin 3   cos 3  sin   cos  14.)__________________ 15.)__________________ Simplify. 16.  csc 2 x 1  cos 2 x  17. sin  x  cot x   sin   x  2  16.)__________________ 17.)__________________ 18. The rate of change of the function f ( x)  csc x  cot x is given by the expression 1  cos x . csc 2 x  csc x cot x . Show that this expression can also be written as sin 2 x Verify. 19. sec 2 x cot x  cot x  tan x 21. cos 3 x sin 2 x  sin 2 x  sin 4 x cos x 22. 23. 1  sec x    csc x sin  x   tan x  24.  20.  cot 2 x  cos 2 x  cot 2 x cos 2 x 1  cos x  sin x 1  cos x   tan  x  sec x  csc x  2 Solve for x. Make sure to check all solutions. 25. 4 cos x  1  2 cos x 26. 1 sec x  1  0 2 25.)__________________ 26.)__________________ 27. 4 tan 2 x  1  tan 2 x 28. sin 2 x  sin x  0 27.)__________________ 28.)__________________ 29. csc x  2 cot x  0 29.)__________________ Solve the following trig equations for [0,2 ) . 30. 2 sin 2 x  3 sin x  1 31. sin 2 x  2 cos x  2 30.)__________________ 31.)__________________ 32. 3 tan 3x  0 33. 3 csc 2 5x  4 32.)__________________ 33.)__________________ Find the exact values of sine, cosine and tangent of the given angle. 34. 345 35. 13 12 34.)__________________ 35.)__________________ Write the expression as the sine, cosine, or tangent of an angle. 36. cos 45 cos120  sin 45 sin 120 37. tan 63  tan118 1  tan 63 tan118 36.)__________________ 37.)__________________ Find the exact value of the trigonometric function given that sin u  3 7 and cos v   . Both u and v are 5 25 in Quadrant II. 38. tanu  v  39. sin u  v  cosu  v  40. 38.)__________________ 39.)__________________ 40.)__________________ Find the value of the expression without using a calculator. 41.  cos cos 1 1  sin 1 0  42.   tan cos 1  1  cos 1 1 41.)__________________ 42.)__________________ Find the exact values of sin 2u, cos 2u, and tan 2u using the double angle formulas. 43. cos u  4 3 ,  u  2 2 5 44. 2  u  tan u   , 9 2 43.)__________________ 44.)__________________ u u u Find the exact values of sin , cos , and tan using the half angle formulas. 2 2 2 45. 11230' 46. 7 8 45.)__________________ 46.)__________________ u u u Find the exact values of sin , cos , and tan using the half angle formulas. 2 2 2 47. tan u  3 21 , u  2 20 48. sec u  6,  2 u  47.)__________________ 48.)__________________ Use the half angle formulas to simplify the expression. 49.  1  cos 8 x 2 50. sin 10 x 1  cos 10 x 49.)__________________ 50.)__________________ Answers 5 1. 6 7. 2.  7 58 58 csc x 3. 8. 16. 1  25. 3  29. 3  3 4. , 2 cot x 5. 2 9. 0,  |sec x| 1 3 tan   2 2 0 ,  , 6. 13. 3 2 4 sec   3 Sin x 11. -tan x 14. sec x  1 15. 1 sin  cos  2 4 cot   -1 18-24. answers will vary  2n, 5  2n 3 26.  2n, 5  2n 3 30.  3  2n, 5  2n 3   5 , 6 2 , 27. 31. 6  6  n, 5  n 6 0 2 6 4 6 2 cos 345  4 tan 345  3  2 36. cos 165 34. 37. tan 55 38. 28. n, sin 11230'  42. 0 43. 2 2 2 45. cos 11230'   2  2 2 sin 46. tan 11230'  1  2 49.  cos 4 x 50. 7  8 35. 117 44 39. 7 2 2  8 2 7 tan  1 2 8 cos tan5 x  3 , 3 13 2 6  12 4 13  6  2 cos  12 4 13 tan  2 3 12 3 5 24 25 7 cos 2u  25 24 tan 2u   7 2 2 2  2 4 5 sin 40. 4 5 36 85 77 cos 2u  85 36 tan 2u   77 sin 2u   41. 1 3  2n 2 0 ,  , 32. sin 345  no solution , , , , , 2 2 6 6 6 6 10. csc   17. 33.  3  5 7 11 cos   2 13 sin   13 3 13 cos   13 13 csc   2 3 cot   2 12. 2 13 13 sin 2u   44. u 7 58  2 58 u 3 58 47. cos   2 58 u 7 tan   2 3 sin u  2 u cos  2 u tan  2 sin 48. 21 6 15 6 35 5 , 3 , 3