765 CHAPTER 7 Review Exercises 31. sin x = 1 10 , cos y = 4 5 , x in quadrant I, y in quadrant IV 32. cos x = 2 9 , sin y = - 1 2 , x in quadrant IV, y in quadrant III Find values of the sine and cosine functions for each angle measure. 33. u, given cos 2u = - 3 4 , 90° 62u 6180° 34. B, given cos 2B = 1 8 , 540° 62B6720° 35. 2x, given tan x = 3, sin x 60 36. 2y, given sec y = - 5 3 , sin y 70 Use the given information to find each of the following. 37. cos u 2 , given cos u = - 1 2 , 90° 6u 6180° 38. sin A 2 , given cos A = - 3 4 , 90° 6A6180° 39. tan x, given tan 2x = 2, p6x 6 3p 2 40. sin y, given cos 2y = - 1 3 , p 2 6y 6p 41. tan x 2 , given sin x = 0.8, 0 6x 6 p 2 42. sin 2x, given sin x = 0.6, p 2 6x 6p Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically. 43. sin 2x + sin x cos x - cos 2x 44. 1 - cos 2x sin 2x 45. sin x 1 - cos x 46. cos x sin 2x 1 + cos 2x 47. 21sin x - sin3 x2 cos x 48. csc x - cot x Verify that each equation is an identity. 49. sin2 x - sin2 y = cos2 y - cos2 x 50. 2 cos3 x - cos x = cos2 x - sin2 x sec x 51. sin2 x 2 - 2 cos x = cos2 x 2 52. sin 2x sin x = 2 sec x 53. 2 cos A - sec A = cos A - tan A csc A 54. 2 tan B sin 2B = sec2 B 55. 1 + tan2 a = 2 tan a csc 2a 56. 2 cot x tan 2x = csc2 x - 2 57. tan u sin 2 u = 2 - 2 cos2 u 58. csc A sin 2 A - sec A = cos 2 A sec A 59. 2 tan x csc 2x - tan2 x = 1 60. 2 cos2 u - 1 = 1 - tan2 u 1 + tan2 u 61. tan u cos2 u = 2 tan u cos2 u - tan u 1 - tan2 u 62. sec2 a - 1 = sec 2a - 1 sec 2a + 1 63. sin2 x - cos2 x csc x = 2 sin3 x - sin x 64. sin3 u = sin u - cos2 u sin u 65. tan 4u = 2 tan 2u 2 - sec2 2u 66. 2 cos2 x 2 tan x = tan x + sin x 67. tan a x 2 + p 4b = sec x + tan x 68. 1 2 cot x 2 - 1 2 tan x 2 = cot x 69. - cot x 2 = sin 2x + sin x cos 2x - cos x 70. sin 3t + sin 2t sin 3t - sin 2t = tan 5t 2 tan t 2
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