Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Trigonometry and Periodic Functions - 7.1 The Inverse Sine, Cosine, and Tangent Functions - 7.1 Assess Your Understanding - Page 451: 18



Work Step by Step

The domain of $\cos^{-1}{x}$ is the range of $\cos{x}$, which is $[−1, 1] $. The range of $\cos^{-1}{x}$ is a specified domain of $\cos{x}$, i.e. $\left[0,\pi \right]$. We know that if $\cos y=x$, then $\cos^{-1}(x)=y.$ We know that $\cos(\pi)=-1$, hence $\cos^{-1}(-1)=\pi.$
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