Answer
$-\frac{\pi}{6}$
Work Step by Step
Use the properties of an inverse function, $sin^{-1}(cos(\frac{2\pi}{3}))=sin^{-1}(-cos(\frac{\pi}{3}))=sin^{-1}(-sin(\frac{\pi}{6}))=sin^{-1}(sin(-\frac{\pi}{6}))=-\frac{\pi}{6}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Chapter Review - Review Exercises - Page 527: 18
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