Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Test - Page 287: 7

Answer

Since $\frac{5\pi}{6} \gt \frac{\pi}{2}$, then $arcsin(sin~\frac{5\pi}{6}) \neq \frac{5\pi}{6}$

Work Step by Step

$arcsin(sin~\frac{5\pi}{6}) = arcsin(0.5) = \frac{\pi}{6}$ The domain of arcsin is $[-\frac{\pi}{2}, \frac{\pi}{2}]$ Since $\frac{5\pi}{6} \gt \frac{\pi}{2}$, then $arcsin(sin~\frac{5\pi}{6}) \neq \frac{5\pi}{6}$
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