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 - Page 708: 37



Work Step by Step

Solve for radians, then convert to degrees. $y=\tan^{-1} x$ 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 $y =-\displaystyle \frac{\pi}{4}$ To convert radians to degrees, multiply y with $\displaystyle \frac{180^{o}}{\pi}$ $\displaystyle \theta=-\frac{\pi}{4}\cdot\frac{180^{o}}{\pi}=-45^{o}$
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