Precalculus (10th Edition)

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

Chapter 7 - Analytic Trigonometry - 7.3 Trigonometric Equations - 7.3 Assess Your Understanding - Page 466: 49

Answer

$1.37, 4.51$.

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. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$. After using a calculator in radian mode the solutions for $\tan^{-1}{5}$ is $1.37$ (given by the calculator) and because the tan function has a period of $\pi$ the second solution is: $1.37+\pi\approx4.51$.
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