A-37 Answers to Selected Exercises 37. sin u = - 27 4 ; cos u = 3 4 ; tan u = - 27 3 ; cot u = - 327 7 ; csc u = - 427 7 39. C 41. E 43. B 45. sin u = {22x + 1 x + 1 47. sin x = {21 - cos2 x 49. tan x = {2sec2 x - 1 51. csc x = { 21 - cos2 x 1 - cos2 x In Exercises 53 – 77, there may be more than one possible answer. 53. cos u 55. 1 57. cot u 59. cos2 u 61. sec u - cos u 63. - cot u + 1 65. sin2 u cos2 u 67. tan u sin u 69. cot u - tan u 71. cos2 u 73. tan2 u 75. - sec u 77. sec2 u 79. 2526 - 60 12 ; -2526 - 60 12 81. identity 83. not an identity 85. y = - sin 2x 86. It is the negative of y = sin 2x. 87. y = cos 4x 88. It is the same function. 89. (a) y = - sin 4x (b) y = cos 2x (c) y = 5 sin 3x 90. Students who ignore negative signs will enjoy graphing cosine and secant functions containing a negative coefficient of x in the argument, because it can be ignored and the graph will still be correct. 7.2 Exercises 1. B 3. A 5. 1 7. -sin u 9. cot u; cos u 11. csc u sec u 13. 1 + sec x 15. 1 17. 1 - 2 sin a cos a 19. 2 + 2 sin t 21. -2 cot x csc x 23. 1sin u + 121sin u - 12 25. 4 sin x 27. 12 sin x + 121sin x + 12 29. 1cos2 x + 122 31. 1sin x - cos x211 + sin x cos x2 33. sin u 35. 1 37. tan2 b 39. tan2 x 41. sec2 x 43. cos2 x 89. 1sec u + tan u211 - sin u2 = cos u 91. cos u + 1 sin u + tan u = cot u 93. identity 95. not an identity 101. (a) I = k11 - sin2 u2 (b) When u = 0, cos u = 1, its maximum value. Thus, cos2 u will be a maximum and, as a result, I will be maximized if k is a positive constant. 103. –1 0 4 E C L 10–6 The sum of L and C equals 3. 105. E1t2 = 3 7.3 Exercises 1. E 3. D 5. D 7. D 9. B 11. 26 - 22 4 13. 22 - 26 4 15. 22 - 26 4 17. 26 + 22 4 19. 0 21. cot 3° 23. sin 5p 12 25. sec 75° 36′ 27. cos A - p 8 B 29. tan 31. cos 33. csc For Exercises 35–39, other answers are possible. We give the most obvious one. 35. 15° 37. - p 6 39. 20° 41. 26 - 22 4 43. -2 + 23 45. 26 + 22 4 47. 2 - 23 49. 26 + 22 4 51. -26 - 22 4 53. -2 - 23 55. -2 + 23 57. 22 2 59. 1 61. -1 63. - cos u 65. - cos u 67. cos u - 23 sin u 2 69. 22 1sin x - cos x2 2 71. 23 tan u + 1 23 - tan u 73. 22 1cos x + sin x2 2 75. - cos u 77. - tan x 79. 16 65 ; - 56 65 81. 4 - 626 25 ; 4 + 626 25 83. (a) 63 65 (b) 63 16 (c) I 85. (a) 77 85 (b) - 77 36 (c) II 87. (a) 4 22 + 25 9 (b) -25 - 22 2 (c) II 89. sin Ap 2 + uB = cos u 91. tan A p 2 + uB = - cot u 103. (a) 3 (b) 163 and -163 (c) no 105. (a) 425 lb (c) 0° 107. cos190° + u2 = -sin u 108. cos1270° - u2 = -sin u 109. cos1180° + u2 = -cos u 110. cos1270° + u2 = sin u 111. sin1180° + u2 = -sin u 112. tan1270° - u2 = cot u Chapter 7 Quiz [7.1] 1. cos u = 24 25 ; tan u = - 7 24 ; cot u = - 24 7 ; sec u = 25 24 ; csc u = - 25 7 2. cos2 x + 1 sin2 x [7.3] 3. - 26 - 22 4 4. - cos u 5. (a) - 16 65 (b) - 63 65 (c) III [7.1–7.3] 6. -1 + tan x 1 + tan x 7.4 Exercises 1. C 3. B 5. F 7. - 9. + 11. cos 2u = 17 25 ; sin 2u = - 4221 25 13. cos 2x = - 3 5 ; sin 2x = 4 5 15. cos 2u = 39 49 ; sin 2u = - 4255 49 17. cos u = 225 5 ; sin u = 25 5 19. cos u = - 242 12 ; sin u = 2102 12 21. 23 2 23. 23 2 25. - 22 2 27. 1 2 tan 102° 29. 1 4 cos 94.2° 31. - cos 4p 5 33. sin 4x = 4 sin x cos 3 x - 4 sin3 x cos x 35. tan 3x = 3 tan x - tan3 x 1 - 3 tan2 x 37. sin 160° - sin 44° 39. sin p 2 - sin p 6 41. 3 cos x - 3 cos 9x 43. -2 sin 3x sin x 45. -2 sin 11.5° cos 36.5° 47. 2 cos 6x cos 2x 49. 32 + 22 2 51. 2 - 23 53. - 32 + 23 2 55. 210 4 57. 3 59. 350 - 10 25 10 61. -27 63. 25 5 65. - 242 12 67. sin 20° 69. tan 73.5° 71. tan 29.87° 73. cos 9x 75. tan 4u 77. cos x 8 99. cos 4 x - sin4 x = cos 2x 101. 2 tan x 2 - sec2 x = tan 2x 103. sin x 1 + cos x = tan x 2
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