Answer
$\frac{\pi}{4}$
Work Step by Step
$\csc^{-1}{\sqrt2}=\frac{\pi}{4}$, because $\csc{\frac{\pi}{4}}=\sqrt2$ and $\frac{\pi}{4}$ is in the range of $\csc^{-1}{x}$, which is $[-\frac{\pi}{2},\frac{\pi}{2}]$ \ $\{0\}.$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 458: 40
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