College Trigonometry, 2011a

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742 Foundations of <strong>Trigonometry</strong> 47. sin(t) =1whent = π 2 +2πk for any integer k. √ 2 48. cos(t) =− 2 when t = 3π 4 +2πk or t = 5π +2πk for any integer k. 4 49. sin(78.95 ◦ ) ≈ 0.981 50. cos(−2.01) ≈−0.425 51. sin(392.994) ≈−0.291 52. cos(207 ◦ ) ≈−0.891 53. sin (π ◦ ) ≈ 0.055 54. cos(e) ≈−0.912 55. θ =60 ◦ , b = √ 3 3 , c = 2√ 3 3 56. θ =45 ◦ , a =3,c =3 √ 2 57. α =57 ◦ , a = 8 cos(33 ◦ ) ≈ 6.709, b =8sin(33 ◦ ) ≈ 4.357 58. β =42 ◦ , c = 59. The hypotenuse has length 6 sin(48 ◦ ) ≈ 8.074, a = √ c 2 − 6 2 ≈ 5.402 4 cos(12 ◦ ) ≈ 4.089. 60. The side adjacent to θ has length 5280 cos(78.123 ◦ ) ≈ 1086.68. 61. The hypotenuse has length 117.42 sin(59 ◦ ) ≈ 136.99. 62. The side opposite θ has length 10 sin(5 ◦ ) ≈ 0.872. 63. The side adjacent to θ has length 10 cos(5 ◦ ) ≈ 9.962. 64. The hypotenuse has length c = √ c 2 − 306 2 ≈ 398.797. 306 sin(37.5 ◦ ) ≈ 502.660, so the side adjacent to θ has length 65. cos(θ) =− 7 , sin(θ) =24 25 25 66. cos(θ) = 3 5 , sin(θ) =4 5 67. cos(θ) = 5√ 106 106 , sin(θ) =−9√ 106 106 68. cos(θ) =− 2√ 5 25 , sin(θ) =−11√ 5 25 69. r =1.125 inches, ω = 9000π radians minute , x =1.125 cos(9000πt), y =1.125 sin(9000πt). Here x and y are measured in inches and t is measured in minutes.
10.2 The Unit Circle: Cosine and Sine 743 70. r =28inches,ω = 2π radians 3 second , x =28cos( 2π 3 t) , y =28sin ( 2π 3 t) .Herex and y are measured in inches and t is measured in seconds. 71. r =1.25 inches, ω = 14400π radians minute , x =1.25 cos(14400πt), y =1.25 sin(14400πt). Here x and y are measured in inches and t is measured in minutes. 72. r =64feet,ω = 4π radians 127 second , x =64cos( 4π 127 t) , y =64sin ( 4π 127 t) .Herex and y are measured in feet and t is measured in seconds
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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
Page 7 and 8: xi text and we have gone to great l
Page 9 and 10: Chapter 10 Foundations of Trigonome
Page 11 and 12: 10.1 Angles and their Measure 695 k
Page 13 and 14: 10.1 Angles and their Measure 697 2
Page 17 and 18: 10.1 Angles and their Measure 701 T
Page 19 and 20: 10.1 Angles and their Measure 703 y
Page 21 and 22: 10.1 Angles and their Measure 705 y
Page 23 and 24: 10.1 Angles and their Measure 707 h
Page 27 and 28: 10.1 Angles and their Measure 711 I
Page 33 and 34: 10.2 The Unit Circle: Cosine and Si
Page 53 and 54: 30 ◦ 1 10.2 The Unit Circle: Cosi
Page 57: 10.2 The Unit Circle: Cosine and Si
Page 61 and 62: 10.3 The Six Circular Functions and
Page 87 and 88: 10.4 Trigonometric Identities 771 f
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Page 107 and 108: 10.5 Graphs of the Trigonometric Fu
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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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10.7 Trigonometric Equations and In
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Chapter 11 Applications of Trigonom
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11.1 Applications of Sinusoids 883
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11.2 The Law of Sines 897 minimizes
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11.2 The Law of Sines 899 a angle-s
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11.2 The Law of Sines 901 determine
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11.2 The Law of Sines 903 Let x den
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11.2 The Law of Sines 905 24. Along
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11.2 The Law of Sines 907 33. The a
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11.2 The Law of Sines 909 25. (a)
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11.3 The Law of Cosines 911 of B ar
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11.3 The Law of Cosines 913 the pre
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11.3 The Law of Cosines 915 A 2 = =
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11.3 The Law of Cosines 917 22. A n
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11.4 Polar Coordinates 919 11.4 Pol
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11.4 Polar Coordinates 921 The poin
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11.4 Polar Coordinates 923 4. We mo
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11.4 Polar Coordinates 925 Solution
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11.4 Polar Coordinates 927 Solution
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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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