766 CHAPTER 7 Trigonometric Identities and Equations 71. Graph the inverse sine, cosine, and tangent functions, indicating the coordinates of three points on each graph. Give the domain and range for each. Concept Check Determine whether each statement is true or false. If false, tell why. 72. The ranges of the inverse tangent and inverse cotangent functions are the same. 73. It is true that sin 11p 6 = - 1 2 , and therefore arcsin A - 1 2B = 11p 6 . 74. For all x, tan1tan-1 x2 = x. Find the exact value of each real number y. Do not use a calculator. 75. y = sin-1 22 2 76. y = arccos a- 1 2b 77. y = tan-1 A -23 B 78. y = arcsin1-12 79. y = cos-1 a- 22 2 b 80. y = arctan 23 3 81. y = sec-11-22 82. y = arccsc 223 3 83. y = arccot1-12 Give the degree measure of u. Do not use a calculator. 84. u = arccos 1 2 85. u = arcsin ¢- 23 2 ≤ 86. u = tan-1 0 Use a calculator to approximate each value in decimal degrees. 87. u = arctan 1.7804675 88. u = sin-11-0.660453202 89. u = cos-1 0.80396577 90. u = cot-1 4.5046388 91. u = arcsec 3.4723155 92. u = csc-1 7.4890096 Evaluate each expression without using a calculator. 93. cos1arccos1-122 94. sin ¢arcsin ¢- 23 2 ≤≤ 95. arccos acos 3p 4 b 96. arcsec1sec p2 97. tan-1 atan p 4b 98. cos-11cos 02 99. sin aarccos 3 4b 100. cos1arctan 32 101. cos1csc-11-222 102. sec a2 sin-1 a- 1 3bb 103. tan aarcsin 3 5 + arccos 5 7b Write each trigonometric expression as an algebraic expression in u, for u 70. 104. cos ¢arctan u 21 - u2≤ 105. tan ¢arcsec 2u2 + 1 u ≤ Solve each equation over the interval 30, 2p2. Write solutions as exact values or to four decimal places, as appropriate. 106. sin2 x = 1 107. 2 tan x - 1 = 0 108. 3 sin2 x - 5 sin x + 2 = 0 109. tan x = cot x 110. sec2 2x = 2 111. tan2 2x - 1 = 0
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