NAME_________________________________________DATE



NAME_________________________________________DATE___________________

ALGEBRA2 MRS. BINASO

CHAPTER 15: TRIGONOMETRIC IDENTITIES AND EQUATIONS

Show all work on loose leaf.

1. If sin θ = [pic] and θ is located in quadrant I, find cos θ.

2. If cos θ = [pic] and θ is located in quadrant IV, find sin θ.

3. If sin θ = [pic] and tan θ < 0, find cos θ.

4. If cos θ = [pic] and θ is located in quadrant III, find sin θ and tan θ.

Express each of the following as a single term containing one function or constant.

5. sin x cot x 6. sin θ csc θ cot θ 7. cos x tan x csc x

8. 2 – 2cos2θ 9. cos x (1 + tan2x) 10. cos θ sec θ – cos2θ

11. [pic] 12. [pic] 13. [pic]

14. [pic] 15. [pic] 16. [pic]

Prove that each of the following equations is an identity.

17. tan x cos x = sin x 18. tan x csc x = sec x 19. [pic]

20. [pic] 21. sin θ + cot θ cos θ = csc θ

22. 1 – cos2x = sin x cos x tan x 23. (sin x – cos x)2 = 1 – 2 sin x cos x

24. cos2x = sec2x – tan2x – sin2x 25. [pic]

26. sin 2x = 2 cot x sin2x 27. [pic]

28. [pic] 29. [pic]

Solve each equation for all values of the variable in the interval between 0˚ and 360˚.

30. 3 cos θ = cos θ – 1 31. -2 sin θ – [pic] = 0 32. 3 cos θ + 5 = 0

33. 3(sin θ – 1) = 0 34. cot θ + 2 = 2 cot θ + 3

35. cos2θ – cos θ = 0 36. sin2θ + 3 sin θ + 2 = 0

37. cos2θ – 2 cos θ = 3 38. sec2θ = sec θ + 2

39. 3 sin θ + [pic] = 4 40. cos2θ – cos θ + 3 = 0

41. sin2θ + 5 sin θ – 1 = 0 42. cos2θ = 3 cos θ – 1

43. sin2θ + 4 cos θ = 3 44. 2 cos2θ + 3 sin θ = 0

45. cos θ – sin2θ = 1 46. cos 2θ + cos θ = 0

47. 2 sin θ = 2 + cos 2θ 48. cos 2θ = cos θ + 2

Express each of the following in terms of sin θ or cos θ.

49. sin (θ – π) 50. [pic]

If sin x = [pic], sin y = [pic], and x and y are each in quadrant I, find the value of each of the following.

51. sin (x + y) 52. cos (x – y) 53. tan (x + y)

Given the following values, find cos 2θ.

54. sin θ = [pic] 55. cos θ = [pic]

Find each value.

56. [pic] 57. Arc sin [pic] 58. arc cos [pic]

59. Arc cos [pic] 60. Arc sin [pic] 61. arc tan [pic]

62. sin (Arc tan 1) 63. sin [pic] 64. sin [pic]

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