Precalculus (10th Edition)

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

Chapter 7 - Analytic Trigonometry - 7.1 The Inverse Sine, Cosine, and Tangent Functions - 7.1 Assess Your Understanding - Page 450: 12



Work Step by Step

This is the definition of the inverse tangent function, hence it is true. The inverse tangent function gives from the result of the tangent function the original angle. 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. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$.
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