College Trigonometry, 2011a

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878 Foundations of <strong>Trigonometry</strong> 19. x = π 4 , 5π 4 20. x =0, π 3 ,π,5π 3 21. x = π 6 , π 2 , 5π 6 , 3π 2 22. x = π 6 , 5π 6 , 3π 2 23. x =0, 2π 3 , 4π 3 25. x = 2π 3 , 4π ( ) ( 1 1 3 , arccos , 2π − arccos 3 3) 27. x = 7π 6 , 11π ( ) ( 1 1 6 , arcsin ,π− arcsin 3 3) 24. x = π 3 , 5π 3 26. x = π 6 , 5π 6 28. x = 3π 4 , 7π 4 , arctan ( 1 2 ) ( 1 ,π+arctan 2) 29. x =0, 2π 3 , 4π 3 30. x = π 6 , 5π 6 , π 2 31. x =arctan(2),π+ arctan(2) 32. x = π 6 , 7π 6 , 5π 6 , 11π 6 33. x =0,π, π 4 , 3π 4 , 5π 4 , 7π 4 34. x = π 6 , π 4 , 3π 4 , 5π 6 , 7π 6 , 5π 4 , 7π 4 , 11π 6 35. x = π 2 , 3π 2 36. x =0, π 3 , 2π 3 ,π,4π 3 , 5π 3 37. x = π 3 , 5π 3 38. x = π 2 , 3π 2 39. x = π 6 , π 2 , 5π 6 , 3π 40. x = π 2 6 , 5π 6 , 7π 6 , 3π 2 , 11π 6 41. x = π 8 , 5π 8 , 9π 8 , 13π 42. No solution 8 43. x =0, π 7 , 2π 7 , 3π 7 , 4π 7 , 5π 7 , 6π 7 ,π,8π 7 , 9π 7 , 10π 7 , 11π 7 , 12π 7 , 13π 7 44. x =0, π 2 ,π,3π 2 45. x =0 46. x = π 48 , 11π 48 , 13π 48 , 23π 48 , 25π 48 , 35π 48 , 37π 48 , 47π 48 , 49π 48 , 59π 48 , 61π 48 , 71π 48 , 73π 48 , 83π 48 , 85π 48 , 95π 48 47. x =0, π 48. x = π 2 2 , 11π 6 49. x = π 12 , 17π 50. x =0,π, π 12 3 , 4π 3 51. x = 17π 24 , 41π 24 , 23π 24 , 47π 24 52. x = π 6 , 5π 18 , 5π 6 , 17π 18 , 3π 2 , 29π 18
10.7 Trigonometric Equations and Inequalities 879 53. x =0, π 4 , π 2 , 3π 4 ,π,5π 4 , 3π 2 , 7π 4 54. x =0, π 3 , 2π 3 ,π,4π 3 , 5π 3 55. x =0, π 8 , 3π 8 , 5π 8 , 7π 8 ,π,9π 8 , 11π 8 , 13π 8 , 15π 8 56. x = π 7 , π 3 , 3π 7 , 5π 7 ,π,9π 7 , 11π 7 , 5π 3 , 13π 7 57. x =0, 2π 7 , 4π 7 , 6π 7 , 8π 7 , 10π 7 , 12π 7 , π 5 , 3π 5 ,π,7π 5 , 9π 5 ( −1+ √ ) ( 5 −1+ √ ) 5 58. x = arcsin ≈ 0.6662,π− arcsin ≈ 2.4754 2 2 59. x = − 1 2 60. x = −1 61. x = 2 3 √ 62. x = − 3 2 63. x =2 √ 2 64. x =6 √ 65. x = ± 3 2 66. x = 1 2 67. x = −1, 0 68. x = − √ 3 [ π 69. [π, 2π] 70. 3 , π ) [ 4π ∪ 2 3 , 3π ) 2 [ 71. 0, π ] [ 2π ∪ 3 3 , 4π ] [ ] 5π [ ∪ 3 3 , 2π 72. 0, π ) ( 3π ∪ 4 4 , 5π ) ( ] 7π ∪ 4 4 , 2π 73. 75. [ π 4 , 3π ] [ 5π ∪ 4 4 , 7π ] 4 ( 0, π ] [ ) ( 2π ∪ 3 3 ,π ∪ π, 4π ] [ ) 5π ∪ 3 3 , 2π 74. 76. [ 0, π ) ( 11π ∪ 2 [ 0, π ] ∪ 3 ] 6 , 2π [ ] 5π 3 , 2π 77. No solution 78. [0, 2π] [ 79. 0, π ] ( π ∪ 4 2 , 3π ) [ ] 7π ∪ 2 4 , 2π 80. [arccot(4),π) ∪ [π + arccot(4), 2π) ( ( ( 1 1 81. 82. arcsin ,π− arcsin 3) 3)) 83. ( − π 6 , π ) 6 [ −π, − π ) [ ∪ − π 2 3 , π ] ( π ] ∪ 3 2 ,π 84. ( − 2π ) ( π 3 , −π ∪ 3 3 , 2π 3 )
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College Trigonometry Version ⌊π
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Table of Contents vii 10 Foundation
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Preface Thank you for your interest
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xi text and we have gone to great l
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Chapter 10 Foundations of Trigonome
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10.1 Angles and their Measure 695 k
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10.1 Angles and their Measure 697 2
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10.1 Angles and their Measure 701 T
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10.1 Angles and their Measure 703 y
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10.1 Angles and their Measure 705 y
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10.1 Angles and their Measure 707 h
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10.1 Angles and their Measure 711 I
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10.2 The Unit Circle: Cosine and Si
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30 ◦ 1 10.2 The Unit Circle: Cosi
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10.3 The Six Circular Functions and
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10.4 Trigonometric Identities 771 f
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10.4 Trigonometric Identities 773 2
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10.4 Trigonometric Identities 779 T
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10.4 Trigonometric Identities 781 R
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10.4 Trigonometric Identities 785 I
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10.5 Graphs of the Trigonometric Fu
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10.6 The Inverse Trigonometric Func
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11.4 Polar Coordinates 929 algebrai
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11.4 Polar Coordinates 931 45. ( )
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11.4 Polar Coordinates 933 5. ( 12,
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11.4 Polar Coordinates 935 13. (
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11.4 Polar Coordinates 937 73. r =7
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11.5 Graphs of Polar Equations 939
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11.6 Hooked on Conics Again 973 11.
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11.6 Hooked on Conics Again 975 Exa
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11.6 Hooked on Conics Again 977 The
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11.6 Hooked on Conics Again 979 We
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11.6 Hooked on Conics Again 983 The
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11.6 Hooked on Conics Again 985 In
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11.6 Hooked on Conics Again 989 2 9
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11.7 Polar Form of Complex Numbers
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11.8 Vectors 1013 Q ′ (1, 7) up 4
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11.8 Vectors 1015 ⃗v + ⃗w = 〈
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11.8 Vectors 1017 ⃗v − ⃗w =
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11.8 Vectors 1019 The remaining pro
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11.8 Vectors 1021 ‖k⃗v‖ = ‖
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11.8 Vectors 1023 at the origin, th
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11.8 Vectors 1025 Geometrically, th
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11.8 Vectors 1027 11.8.1 Exercises
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11.8 Vectors 1029 44. ⃗v = 〈−
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11.8 Vectors 1031 11.8.2 Answers 1.
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11.8 Vectors 1033 47. ‖⃗v‖ =2
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11.9 The Dot Product and Projection
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11.10 Parametric Equations 1049 obj
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11.10 Parametric Equations 1051 2.
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11.10 Parametric Equations 1053 Now
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11.10 Parametric Equations 1057 Our
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11.10 Parametric Equations 1061 Sup
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Index n th root of a complex number
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Index 1071 central angle, 701 chang
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Index 1073 reflective property, 523
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Index 1075 matrix, multiplicative,
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Index 1077 midpoint definition of,
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Index 1079 instantaneous, 161, 472
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Index 1081 inconsistent, 553 indepe
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College Trigonometry, 2011a

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