Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 480: 22



Work Step by Step

The range of $\tan^{-1}{x}$ is $[-\dfrac{ \pi}{2}, \dfrac{\pi}{2}]$. Here, $\cot(\dfrac{2\pi}{3})=\dfrac{ -\sqrt 3}{3}$, because $\tan{(\dfrac{-\pi}{6})}=\dfrac{-\sqrt 3}{3}$ and $\dfrac{-\pi}{6}$ lies in the range of $\tan^{-1}{x}$ . Therefore, we have: $\tan^{-1}(\cot {(\dfrac{2\pi }{3})}]=\tan^{-1} ({\dfrac{- \sqrt 3}{3}})=\dfrac{-\pi}{6}$
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