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In Problems 75-86, find the exact value of each expression. 75. sin sin V3 + cos 2 - + cos 76. sin sin 79. cos(tan + cos'음) 4 3 78. sin sin tan 13

In Problems 75-86, find the exact value of each expression. 75. sin sin V3 + cos 2 - + cos 76. sin sin 79. cos(tan + cos'음) 4 3 78. sin sin tan 13

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 72E
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498 CHAPTER 7 Analytic Trigonometry sin (a + B) 61. sin a cos B - 1 + cot a tan B 60. cos (a + B) + cos (a - B) = 2 cos a cos B cos (a + B) 63. cos a cos B =1- tan a tan B sin (a + B) 62. cos a cos B - tan a + tan B tan a + tan B cos (a - B) 64. sin a cos B sin (a + B) 65. sin (a - B tan a - tan B = cot a + tan B cot a cot B cos (a + B) 66. cos (a - B) 1- tan a tan B %3D 67. cot (a + B) = cot B + cot a 1 + tan a tan B csc a csc B cot a cot B + 1 69. sec (a + B) = 68. cot (a - B) = cot a cot B-1 cot B - cot a 71. sin (a - B) sin (a + B) = sin a - sin? e sec a sec B В) - 1 + tan a tan B 70. sec (a 73. sin (0 + km) = (-1)* sin 0, k any integer 72. cos (a – B) cos (a + B) = cos? a – sin? ß 74. cos (0 + ka) = (-1)k cos 0, k any integer In Problems 75–86, find the exact value of each expression. 76. sin sin-1 V3 + cos 2 75. sin + cos- 77. - cos"! 4 + cos-1 5 3 80. cos tan-1 12 78. sin - tan- 79. cos tan - sin 81. cos 82. cos tan- + cos 3 4 - tan. 83. tan sin- 3 85. tan sin 4 + cos-1 84. tan 86. tan cos1+ sin 5 cos- nia In Problems 87-92, write each trigonometric expression as an algebraic expression containing u and v. Give the restrictions on u and v. 87. cos (cos u + sin¯1 v) 88. sin (sinu - cos v) 89. sin ( tanu – sin' v) 90. cos (tan u + tan-1 v) 91. tan (sin- u – cos v) 92. sec(tanu + cos"1 v) In Problems 93-–98, solve each equation on the interval 0 se < 27. 93. sin 0 – V3 cos 0 = 1 94. V3 sin e + cos 0 = 1 95. sin 0 + cos e = V2 96. sin e - cos e = - V2 97. tan 0 + V3 = sec 0 98. cot e + csc 0 = - V3 Applications and Extensions 99. Show that sin (sin v + cos v) = 1. 100. Show that cos (sin v + cos v) = 0. A 101. Calculus Show that the difference quotient for f(x) = sin x is given by 103. One, Two, Three (a) Show that tan( tan-1 + tan2 + tan" 3) =. (b) Conclude from part (a) that f(x + h) - f(x) sin (x + h) - sin x tan1 + tan12 + tan¬1 3 = " h h sin h = cos x h 1 - cos h - sin x A 102. Calculus Show that the difference quotient for f(x) = cos x is given by h instantaneous power p at time t is given by p(t) = V„Im cos o sin? (wt) - Vmlm sin o sin(w) a f(x + h) – f(x) cos (x + h) - cos x Show that this is equivalent to h sin h = -sin x h 1-cos h cos x P(t) = VmIm sin ( wt) sin(»t – 9) h
Transcribed Image Text:498 CHAPTER 7 Analytic Trigonometry sin (a + B) 61. sin a cos B - 1 + cot a tan B 60. cos (a + B) + cos (a - B) = 2 cos a cos B cos (a + B) 63. cos a cos B =1- tan a tan B sin (a + B) 62. cos a cos B - tan a + tan B tan a + tan B cos (a - B) 64. sin a cos B sin (a + B) 65. sin (a - B tan a - tan B = cot a + tan B cot a cot B cos (a + B) 66. cos (a - B) 1- tan a tan B %3D 67. cot (a + B) = cot B + cot a 1 + tan a tan B csc a csc B cot a cot B + 1 69. sec (a + B) = 68. cot (a - B) = cot a cot B-1 cot B - cot a 71. sin (a - B) sin (a + B) = sin a - sin? e sec a sec B В) - 1 + tan a tan B 70. sec (a 73. sin (0 + km) = (-1)* sin 0, k any integer 72. cos (a – B) cos (a + B) = cos? a – sin? ß 74. cos (0 + ka) = (-1)k cos 0, k any integer In Problems 75–86, find the exact value of each expression. 76. sin sin-1 V3 + cos 2 75. sin + cos- 77. - cos"! 4 + cos-1 5 3 80. cos tan-1 12 78. sin - tan- 79. cos tan - sin 81. cos 82. cos tan- + cos 3 4 - tan. 83. tan sin- 3 85. tan sin 4 + cos-1 84. tan 86. tan cos1+ sin 5 cos- nia In Problems 87-92, write each trigonometric expression as an algebraic expression containing u and v. Give the restrictions on u and v. 87. cos (cos u + sin¯1 v) 88. sin (sinu - cos v) 89. sin ( tanu – sin' v) 90. cos (tan u + tan-1 v) 91. tan (sin- u – cos v) 92. sec(tanu + cos"1 v) In Problems 93-–98, solve each equation on the interval 0 se < 27. 93. sin 0 – V3 cos 0 = 1 94. V3 sin e + cos 0 = 1 95. sin 0 + cos e = V2 96. sin e - cos e = - V2 97. tan 0 + V3 = sec 0 98. cot e + csc 0 = - V3 Applications and Extensions 99. Show that sin (sin v + cos v) = 1. 100. Show that cos (sin v + cos v) = 0. A 101. Calculus Show that the difference quotient for f(x) = sin x is given by 103. One, Two, Three (a) Show that tan( tan-1 + tan2 + tan" 3) =. (b) Conclude from part (a) that f(x + h) - f(x) sin (x + h) - sin x tan1 + tan12 + tan¬1 3 = " h h sin h = cos x h 1 - cos h - sin x A 102. Calculus Show that the difference quotient for f(x) = cos x is given by h instantaneous power p at time t is given by p(t) = V„Im cos o sin? (wt) - Vmlm sin o sin(w) a f(x + h) – f(x) cos (x + h) - cos x Show that this is equivalent to h sin h = -sin x h 1-cos h cos x P(t) = VmIm sin ( wt) sin(»t – 9) h
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