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: 21

Answer

$y =-\displaystyle \frac{\pi}{3}$

Work Step by Step

$y=\sin^{-1}x =\arcsin x$ Domain: $[-1, 1] $ Range: $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ ----------- $y$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ such that $\displaystyle \sin y=-\frac{\sqrt{3}}{2}$ $\displaystyle \sin(-\frac{\pi}{3})=-\frac{\sqrt{3}}{2}\qquad$and$\displaystyle \quad -\frac{\pi}{3}\in[-\frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$, so $y =-\displaystyle \frac{\pi}{3}$
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