Solutions 46: Other Trigonometric Functions

Solutions to Odd-Numbered Exercises

1. Yes, when the reference angle is π4 and the terminal side of the angle is in quadrants I and III. Thus, at x=π4,5π4, the sine and cosine values are equal.

3. Substitute the sine of the angle in for y in the Pythagorean Theorem x2+y2=1. Solve for x and take the negative solution.

5. The outputs of tangent and cotangent will repeat every π units.

7. 233

9. 3

11. 2

13. 1

15. 2

17. 33

19. 233

21. 3

23. 2

25. −1

27. −2

29. 33

31. 2

33. 33

35. −2

37. −1

39. If sint=223,sect=3,csct=324,tant=22,cott=24

41. sect=2,csct=233,tant=3,cott=33

43. 22

45. 3.1

47. 1.4

49. sint=22,cost=22,tant=1,cott=1,sect=2,csct=2

51. sint=32,cost=12,tant=3,cott=33,sect=2,csct=233

53. –0.228

55. –2.414

57. 1.414

59. 1.540

61. 1.556

63. sin(t)0.79

65. csct1.16

67. even

69. even

71. sintcost=tant

73. 13.77 hours, period: 1000π

75. 7.73 inches