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: 22



Work Step by Step

The domain of $\tan^{-1}{x}$ is the range of $\tan{x}$, which is the real numbers. The range of $\tan^{-1}{x}$ is a specified domain of $\tan{x}$, i.e. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$. We know that if $\tan y=x$, then $\tan^{-1}(x)=y.$ We know that $\tan(\frac{\pi}{6})=\frac{\sqrt3}{3}$, hence $\tan^{-1}(\frac{\sqrt3}{3})=\frac{\pi}{6}.$
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