Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.7 Equations Involving Inverse Trigonometric Functions - 7.7 Exercises - Page 728: 6



Work Step by Step

A. From the definition of arctan, x is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ for which $\tan x=-1$ $-\displaystyle \frac{\pi}{2}\not\in (-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}) $ so $-\displaystyle \frac{\pi}{2}$ is NOT the solution . B. From the definition of arcsin, x is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ for which $\sin x=-1.$ $-\displaystyle \frac{\pi}{2}\in [-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ and $\sin x=-1.$ so $-\displaystyle \frac{\pi}{2}$ is the solution. C. From the definition of arccos, x is the number from $[0, \pi]$ for which $\cos x=-1.$ $-\displaystyle \frac{\pi}{2}\in [0, \pi] $and $\displaystyle \cos(-\frac{\pi}{2})=0.$ so $-\displaystyle \frac{\pi}{2}$ is NOT the solution.
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