Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 4 - Section 4.7 - Inverse Trigonometric Functions - 4.7 Problem Set - Page 261: 30

Answer

$-\frac{\pi}{3}$

Work Step by Step

We need to find the angle between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$. We know that $\sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$. Also, $\sin(-x)=-\sin x$ Then $\sin(-\frac{\pi}{3})=-\frac{\sqrt 3}{2}$ The angle is $-\frac{\pi}{3}$. $\arcsin (-\frac{\sqrt 3}{2})=-\frac{\pi}{3}$
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