Answer
$cos^{-1}(-\frac{\sqrt{2}}{2}) = \frac{3\pi}{4}$
Work Step by Step
The domain of $cos^{-1}(x)$ is $[-1, 1]$ and the range is $[0, \pi]$. $cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2}$, so $cos^{-1}(-\frac{\sqrt{2}}{2}) = \frac{3\pi}{4}$.
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 1 - Functions - 1.4 Trigonometric Functions and Their Inverse - 1.4 Exercises - Page 48: 50
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