Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Review Exercises - Page 646: 112


The exact value of expression is $-\frac{\pi }{6}$.

Work Step by Step

To simplify ${{\sin }^{-1}}\left( \cos \frac{2\pi }{3} \right)$, we apply the property: $\left( \cos \frac{\pi }{2}+\theta \right)=-\sin \theta $ Therefore, $\left( \cos \frac{\pi }{2}+\frac{\pi }{6} \right)=-\sin \frac{\pi }{6}$ Then, simplify ${{\sin }^{-1}}\left( -\sin \frac{\pi }{6} \right)$. Apply the inverse property, ${{\sin }^{-1}}\left( -\sin \frac{\pi }{6} \right)=-\frac{\pi }{6}$ Then, ${{\sin }^{-1}}\left( -\sin \frac{\pi }{6} \right)=-\frac{\pi }{6}$. Hence, the exact value of the expression is $-\frac{\pi }{6}$.
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