College Trigonometry, 2011a

10.6 The Inverse Trigonometric Functions 851
( ( 1
79. sec arcsec is undefined.
2))
80. sec (arcsec (0.75)) is undefined.
81. sec (arcsec (117π)) = 117π 82. csc ( arccsc (√ 2 )) = √ 2
( ( ))
( (√ ))
83. csc arccsc − 2√ 3
= − 2√ 3
2
84. csc arccsc is undefined.
3
3
2
( ( π
))
85. csc (arccsc (1.0001)) = 1.0001 86. csc arccsc is undefined.
4
( ( π
))
87. arcsin sin = π 6 6
( ( )) 3π
89. arcsin sin = π 4 4
( ( )) 4π
91. arcsin sin = − π 3 3
( ( )) 2π
93. arccos cos = 2π 3 3
( (
95. arccos cos − π ))
= π 6 6
( ( π
))
97. arctan tan = π 3 3
( (
88. arcsin sin − π ))
= − π 3 3
( ( )) 11π
90. arcsin sin = − π 6 6
( ( π
))
92. arccos cos = π 4 4
( ( )) 3π
94. arccos cos = π 2 2
( ( )) 5π
96. arccos cos = 3π 4 4
( (
98. arctan tan − π ))
= − π 4 4
( ( π
))
99. arctan (tan (π)) = 0 100. arctan tan is undefined
2
( ( 2π
101. arctan tan
3
))
= − π 3
( ( π
))
102. arccot cot = π 3 3
( (
103. arccot cot − π ))
= 3π 4 4
( ( )) 3π
105. arccot cot = π 2 2
( ( π
))
107. arcsec sec = π 4 4
( ( )) 5π
109. arcsec sec = 7π 6 6
( ( )) 5π
111. arcsec sec = π 3 3
104. arccot (cot (π)) is undefined
( ( )) 2π
106. arccot cot = 2π 3 3
( ( )) 4π
108. arcsec sec = 4π 3 3
( (
110. arcsec sec − π ))
is undefined.
2
( ( π
))
112. arccsc csc = π 6 6