Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.5 Inverse Circular Functions - 7.5 Exercises: 18

Answer

$-\displaystyle \frac{\pi}{4}$

Work Step by Step

$y=\tan^{-1} x =\arctan x$ Domain: $(-\infty, \infty) $ Range: $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ ----------- $y$ is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ such that $\tan y=-1$ $\displaystyle \tan(-\frac{\pi}{4})=-1\qquad$and$\displaystyle \quad -\frac{\pi}{4}\in(-\frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ so $\tan^{-1} (-1) =-\displaystyle \frac{\pi}{4}$
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