C H A P T E R 5 Analytic Trigonometry

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440 Chapter 5 <strong>Analytic</strong> <strong>Trigonometry</strong> 9. is in Quadrant II. cos x 1 sin2 1 x 1 9 22 sin x 3 1 1 ⇒ sin x , tan x 2 ⇒ x 3 3 4 10. x is in Quadrant I. cos x 1 sec x 4, sin x > 0 1 sec x 4 cot x 1 tan x 1 24 22 sec x 1 cos x 1 223 32 4 csc x 1 1 3 sin x 13 11. tan 2, sin < 0 ⇒ is in Quadrant III. 13. sec tan 2 1 4 1 5 cos 1 1 sec 5 5 5 sin 1 cos 2 1 2 1 5 5 25 5 csc 1 sin 5 2 cot 1 1 tan 2 sin 1, cot 0 ⇒ 3 2 cos 1 sin 2 0 sec is undefined. tan is undefined. csc 1 sin x 1 1 4 2 15 4 tan x sin x 15 cos x 4 4 15 1 csc x 1 4 415 sin x 15 15 cot x 1 1 15 tan x 15 15 12. csc 5, cos < 0 is in Quadrant III. sin 1 csc 1 5 cos 1 1 5 2 26 5 tan sin cos 1 5 6 5 26 12 sec 1 5 cos 26 56 12 cot 1 12 26 tan 6 14. tan is undefined, sin > 0. 2 tan sin 1 0 2 1 csc 1 1 sin sec 1 is undefined. cos cot sin is undefined ⇒ cos 0 cos cos 0 0 sin 1 1 15. sec x cos x sec x 1 sec x sin x 16. tan x csc x cos x The expression is matched with (d). Matches (a). 1 1 sec x sin x cos x 17. cot 2 x csc 2 x cot 2 x 1 cot 2 x 1 The expression is matched with (b). 18. 1 cos Matches f. 2 xcsc x sin2 x 1 sin x sin x
19. 22. 24. 26. sinx sin x tan x 20. cosx cos x The expression is matched with (e). Matches (c). cos 2 x sin2 x cos 2 x sin 2 x sin2 x cos x cot x 21. cos2 x sin x Matches (c). cos 2 xsec 2 x 1 cos 2 xtan 2 x 23. cos x cot x sec x sin x Matches (a). 1 1 csc x 25. cos x sin x cos 2 2 x cos x Matches (d). sin2 x cos x sin 28. cos tan cos sin cos 29. sin x sin x tan x sin x 27. cos x 30. sec2 x1 sin2 x sec2 x sec2 x sin2 x 31. 32. 34. 36. csc 1sin sec 1cos sec 2 x 1 cos 2 x sin2 x sec 2 x sin2 x cos 2 x sec 2 x tan 2 x 1 cos cot sin 33. Section 5.1 Using Fundamental Identities 441 sin x sec x sin x The expression is matched with f. 1 tan x cos x The expression is matched with (b). sec 4 x tan 4 x sec 2 x tan 2 xsec 2 x tan 2 x sec 2 x 1 sin 2 x tan2 x sin 2 x sin2 x cos 2 x sec 2 x tan 2 x1 sec 2 x tan 2 x The expression is matched with (e). cot sec 1 sin 2 x sec2 x cos sin 1 1 csc cos sin sin csc sin sin 1 sin sin2 cot x cos xsin x csc x 1sin x cos x sin x sin x 1 cos x 1 sin 2 cos 2 1 sin2 x csc 2 x 1 cos2 x cot 2 x cos2 x tan 2 x cos 2 x sin2 x cos 2 x 1 tan2 1 x 1 sec2 x 1 1cos2 x cos2 sin 1 x 35. sec sin cot tan cos tan2 sec2 sin2 cos2 1 sec2 sin2 cos 2 1 1cos2 sin2 cos2 sin2 cos 2 37. 1 cos sin 1 cos sin cos x sec x sin xsec x 2 sin 2 x sin x 1 sin x tan x cos x cos x
Page 1 and 2: CHAPTER 5 Analytic Trigonometry Sec
Page 3: 1. sin x 3 , cos x 1 2 2 tan x si
Page 7 and 8: 53. sin 4 x cos 4 x sin 2 x cos
Page 9 and 10: 74. 75. 76. y 1 sec x csc x tan x
Page 11 and 12: 88. 90. 92. 94. 96. cos 1 sin 2
Page 13 and 14: Section 5.1 Using Fundamental Ident
Page 15 and 16: 5. cos 2 sin 2 1 sin 2 sin 2
Page 17 and 18: 28. 30. 32. 33. 1 sin y1 siny 1
Page 19 and 20: 43. (a) (b) (c) 45. (a) 47. (b) (c)
Page 21 and 22: 61. 63. 65. 67. 2 3i 26 2 3i 2
Page 23 and 24: 5. 7. 2 sin2 x sin x 1 0 6. csc4
Page 25 and 26: 24. 26. 28. 30. 2 sin 2 x 2 cos x
Page 27 and 28: 40. 42. 44. sin x 2 3 2 x 2 4 2n
Page 29 and 30: 56. 3 tan 2 x 4 tan x 4 0 tan x
Page 31 and 32: 64. (a) f x 2 sin x cos 2x max: 0
Page 33 and 34: 75. —CONTINUED— 76. (a) (b) The
Page 35 and 36: Section 5.4 Sum and Difference Form
Page 37 and 38: 10. 12. 255 300 45 11. sin 255 sin3
Page 39 and 40: 16. 105 30 135 17. sin30 135 sin
Page 41 and 42: 21. 22. 13 12 3 sin 4 3 cos 4 3 ta
Page 43 and 44: 37. 39. 41. sinu v sin u cos v c
Page 45 and 46: 53. 54. Let 55. 57. 59. cosarccos x
Page 47 and 48: 69. 70. 71. sin x cos 3 cos x sin
Page 49 and 50: 75. 76. y 1 3 1 sin 2t cos 2t 4 5
Page 51 and 52: 93. y1= m1x + b1 α y θ δ β y2=
Page 53 and 54: 97. 99. f x 5x 3 98. f 1 x y 5x
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Section 5.5 Multiple-Angle and Prod
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15. 17. tan 2x cot x 0 16. 2 tan
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26. 27. 28. 29. cot u 4, 3 2 < u <
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33. 1 sin 1 cos 2x1 cos 2x1 cos
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45. 47. 48. 49. sin 1 sin 8 2 4
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1 cos 6x 55. 2 sin 3x 57. 59. 1
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73. 75. cos sin 1 sin 5 sin 3
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91. 93. 95. 97. 99. sin 2 5 13 2
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111. 112. 114. −2 2 −3 cos 3 c
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125. (a) ) (b) y 4 sin x cos x 2
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134. (a) The supplement is 180 109
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24. 26. sin12 x cos x 1 sin x cos
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49. 50. 52. tan 2 tan 12 0 tan
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61. 7 5 4 13 3 4 12 13 1 57 3
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77. sin 4x 2 sin 2x cos 2x 78. 22
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88. tan u 5 3 , < u < 8 2 sin u
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103. 0 2 −2 Review Exercises for
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1. —CONTINUED— 2. 4. (b) cos si
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7. The hypotenuse of the larger rig
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14. (a) cos3 cos2 (b) cos4 cos2
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C H A P T E R 5 Analytic Trigonometry

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