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sin -Cos sin+ cos e sec e csc e 81. sin e cos sin'e+ cos'e sin ở+ cos -1- sin e cos @ sin' e cos + sin e 86. sin' e cot e+ cos cos'e sin an'e + sin e+ cos e 1+ cose os'e tan -cot 8 os 89. 1+ sin e cos 8 sin e 91. (a sin e+ b cos )+ (a cos 8-b sin e)-+ tan a + tan B 93 cot a + cot B tan a tan B

sin -Cos sin+ cos e sec e csc e 81. sin e cos sin'e+ cos'e sin ở+ cos -1- sin e cos @ sin' e cos + sin e 86. sin' e cot e+ cos cos'e sin an'e + sin e+ cos e 1+ cose os'e tan -cot 8 os 89. 1+ sin e cos 8 sin e 91. (a sin e+ b cos )+ (a cos 8-b sin e)-+ tan a + tan B 93 cot a + cot B tan a tan B

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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486 CHAPTER 7 Analytic Trigonometry (sec v - tan v) +1 79. csc v(sec v- tan v) - 2 tan v I+ sin e 78. 1- sine (sec e+ tan e) sec e 1+ sin e 77 1- sin e cos e sin ở sin e - cos 0 sin ở + cos 0 81. - sec e csc e sin 0 see' v- tany+ tan v 80. -sin v + cos v cos e sec v sin'e + co'e -1- sin e cos e sin e+ cos 8 82. sin e cos e- sin e cos e sec e cse e sin e + cos a cos e + sin e- sin' e 86. - cot e+ co sin'e+ cos'e sec e- sin e tan e-1 cose - sine 8S. - cose sin e 84. 1- 2 cos' e (2 cose - 1) 85. 1- tan'e 1- 2 cos' e sin ecos e tan e- cor e sin e cos e 1+ sin 8 + cos 01+ cos 6 89. 1+ sin e -cos 0 sin e -1- 2 sin e 87. cos e - sin'e 1+ cos e + sin 91. (a sin e + b cos 0)+ (a cos 0- b sin 0)2 - a² +2 90. 1+ cos e- sin sec e + tan e tan a + tan B 93. cot a + cot 8 fan a tan 8 92. (2a sin e cos 0) + a'(cos e - sin 0)? = a 94. (tan a + tan 8) (1 - cot a cot B) + (cot a + cot B) (1 - tan a tan B) =0 95. (sin a + cos 8) + (cos 8 + sin a) (cos B - sin a) = 2 cos B(sin a + cos B) 96. (sin a - cos 8) + (cos 8 + sin a) (cos 8 - sin a) - -2 cos B(sin a - cos B) 97. In sec e- -In Jcos e 98. In tan e- In sin e - In cos e 99. In |1 + cos e + In |1 - cos e - 2 In sin e 100. In sec e + tan e + In sec e - tan e -0 In Problems 101-104, show that the functions fand g are identically equal. 101. f(x) - sin x- tan x g(x) = secx - cos x 102. f(x) cos x. cot x g(x) - csc x - sin x 1- sin e cos e 1+ sin e 103. f(0) g(0) = 0 cos e - cos e 104. f(0) - tan 0 + sec 6 g(@) = %3D 1- sin e A 105. Show that V16 + 6 tan 0-4 sec 6 if - 3m r-<0< A 106. Show that V9 soc e - 9 = 3 tan ở if S 0 < くう 2 Applications and Extensions 107. Searchlights A searchlight at the grand opening of a new car dealership casts a spot of light on a wall located 75 meters from the searchlight. The acceleration F of the spot of light is found to be F= 1200 sec 0(2 sec²e - 1). Show that this is 108. Optical Measureanent Optical methods of measurement often rely on the interference of two light waves. If two light waves, identical except for a phase lag, are mixed together, the resulting intensity, or irradiance, is given by (1+ sin e cos' e Source: Adapted from Hibbeler, Engineering Mechanics: equivalent to 7 = 1200 (csc e - 1) (sec e + tan 0) I, = 44 csc 0 sec e Show that this is equivalent to I, = (2A cos 0). Source: Experimental Techniques, July/August 2002 Dynamics, 13th ed., Pearson © 2013. 109. Challenge Problem Prove: sin(-x) = -sin"'x 110. Challenge Problem Prove: cot"x = tan Explaining Concepts: Discussion and Writing 111. Write a few paragraphs outlining your strategy for establishing 113. Why do you think it is usually preferable to start wi identities 112. Write down the three Pythagorean Identities side containing the more complicated expression establishing an identity? 114. Make up an identity that is not a basic identity. - Retain Your Knowledge Problems 115-124 are based on material learned earlier in the course. The purpose of these prel wour mind so that you are better prepared for the final exam Retake Use Photo
Transcribed Image Text:486 CHAPTER 7 Analytic Trigonometry (sec v - tan v) +1 79. csc v(sec v- tan v) - 2 tan v I+ sin e 78. 1- sine (sec e+ tan e) sec e 1+ sin e 77 1- sin e cos e sin ở sin e - cos 0 sin ở + cos 0 81. - sec e csc e sin 0 see' v- tany+ tan v 80. -sin v + cos v cos e sec v sin'e + co'e -1- sin e cos e sin e+ cos 8 82. sin e cos e- sin e cos e sec e cse e sin e + cos a cos e + sin e- sin' e 86. - cot e+ co sin'e+ cos'e sec e- sin e tan e-1 cose - sine 8S. - cose sin e 84. 1- 2 cos' e (2 cose - 1) 85. 1- tan'e 1- 2 cos' e sin ecos e tan e- cor e sin e cos e 1+ sin 8 + cos 01+ cos 6 89. 1+ sin e -cos 0 sin e -1- 2 sin e 87. cos e - sin'e 1+ cos e + sin 91. (a sin e + b cos 0)+ (a cos 0- b sin 0)2 - a² +2 90. 1+ cos e- sin sec e + tan e tan a + tan B 93. cot a + cot 8 fan a tan 8 92. (2a sin e cos 0) + a'(cos e - sin 0)? = a 94. (tan a + tan 8) (1 - cot a cot B) + (cot a + cot B) (1 - tan a tan B) =0 95. (sin a + cos 8) + (cos 8 + sin a) (cos B - sin a) = 2 cos B(sin a + cos B) 96. (sin a - cos 8) + (cos 8 + sin a) (cos 8 - sin a) - -2 cos B(sin a - cos B) 97. In sec e- -In Jcos e 98. In tan e- In sin e - In cos e 99. In |1 + cos e + In |1 - cos e - 2 In sin e 100. In sec e + tan e + In sec e - tan e -0 In Problems 101-104, show that the functions fand g are identically equal. 101. f(x) - sin x- tan x g(x) = secx - cos x 102. f(x) cos x. cot x g(x) - csc x - sin x 1- sin e cos e 1+ sin e 103. f(0) g(0) = 0 cos e - cos e 104. f(0) - tan 0 + sec 6 g(@) = %3D 1- sin e A 105. Show that V16 + 6 tan 0-4 sec 6 if - 3m r-<0< A 106. Show that V9 soc e - 9 = 3 tan ở if S 0 < くう 2 Applications and Extensions 107. Searchlights A searchlight at the grand opening of a new car dealership casts a spot of light on a wall located 75 meters from the searchlight. The acceleration F of the spot of light is found to be F= 1200 sec 0(2 sec²e - 1). Show that this is 108. Optical Measureanent Optical methods of measurement often rely on the interference of two light waves. If two light waves, identical except for a phase lag, are mixed together, the resulting intensity, or irradiance, is given by (1+ sin e cos' e Source: Adapted from Hibbeler, Engineering Mechanics: equivalent to 7 = 1200 (csc e - 1) (sec e + tan 0) I, = 44 csc 0 sec e Show that this is equivalent to I, = (2A cos 0). Source: Experimental Techniques, July/August 2002 Dynamics, 13th ed., Pearson © 2013. 109. Challenge Problem Prove: sin(-x) = -sin"'x 110. Challenge Problem Prove: cot"x = tan Explaining Concepts: Discussion and Writing 111. Write a few paragraphs outlining your strategy for establishing 113. Why do you think it is usually preferable to start wi identities 112. Write down the three Pythagorean Identities side containing the more complicated expression establishing an identity? 114. Make up an identity that is not a basic identity. - Retain Your Knowledge Problems 115-124 are based on material learned earlier in the course. The purpose of these prel wour mind so that you are better prepared for the final exam Retake Use Photo
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