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: 50


$0.46, 3.61$

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 $\cot^{-1}(x)=\tan^{-1}{\frac{1}{x}}$. After using a calculator in radian mode the solutions for $\theta=\cot^{-1}{2}=\tan^{-1}{\frac{1}{2}}=0.463647609\approx0.46$ (given by the calculator) and because the cotangent function has a period of $\pi$, the second solution is: $0.463647609+\pi\approx 3.61$.
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