547 5.2 Trigonometric Functions An equation of the terminal side of an angle u in standard position is given with a restriction on x. Sketch the least positive such angle u, and find the values of the six trigonometric functions of u. See Example 3. 43. 2x + y = 0, x Ú 0 44. 3x + 5y = 0, x Ú 0 45. -4x + 7y = 0, x … 0 46. 6x - 5y = 0, x Ú 0 47. x + y = 0, x Ú 0 48. x - y = 0, x Ú 0 49. -23x + y = 0, x … 0 50. 23x + y = 0, x … 0 Find the indicated function value. If it is undefined, say so. See Example 4. 51. cos 90° 52. sin90° 53. tan180° 54. cot 90° 55. sec 180° 56. csc 270° 57. sin1-270°2 58. cos1-90°2 59. cot 540° 60. tan450° 61. csc1-450°2 62. sec1-540°2 63. sin1800° 64. cos 1800° 65. csc 1800° 66. cot 1800° 67. sec 1800° 68. tan1800° 69. cos1-900°2 70. sin1-900°2 Use trigonometric function values of quadrantal angles to evaluate each expression. An expression such as cot2 90° means 1cot 90°22, which is equal to 02 = 0. 71. cos 90° + 3 sin270° 72. tan0° - 6 sin90° 73. 3 sec 180° - 5 tan360° 74. 4 csc 270° + 3 cos 180° 75. tan360° + 4 sin180° + 5 cos2 180° 76. 5 sin2 90° + 2 cos2 270° - tan360° 77. -2 sin4 0° + 3 tan2 0° 78. -3 sin4 90° + 4 cos3 180° 79. sin21-90°2 + cos21-90°2 80. cos21-180°2 + sin21-180°2 If n is an integer, n # 180° represents an integer multiple of 180°, 12n + 12 # 90° represents an odd integer multiple of 90°, and so on. Determine whether each expression is equal to 0, 1, or -1, or is undefined. 81. cos312n + 12 # 90°4 82. sin3n # 180°4 83. tan3n # 180°4 84. sin3270° + n # 360°4 85. tan312n + 12 # 90°4 86. cot3n # 180°4 Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 5. 87. sec u, given that cos u = 2 3 88. sec u, given that cos u = 5 8 89. csc u, given that sinu = - 3 7 90. csc u, given that sinu = - 8 43 91. cot u, given that tanu = 5 92. cot u, given that tanu = 18 93. sinu, given that csc u = 28 2 94. sinu, given that csc u = 224 3 95. sinu, given that csc u = 1.25 96. cos u, given that sec u = 8 Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 6. 97. 74° 98. 84° 99. 218° 100. 195° 101. 178° 102. 125° 103. -80° 104. -15° 105. 855° 106. 1005° 107. -345° 108. -640°
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