Answer
$\frac{1}{2}$
Work Step by Step
Let $\sin^{-1}(\frac{\sqrt 3}{2})= y$. Then,
$\sin y=\frac{\sqrt 3}{2}= \sin \frac{\pi}{3}$.
This implies $y= \frac{\pi}{3}$.
Therefore, $\cos(\sin^{-1}\frac{\sqrt 3}{2})= \cos(\frac{\pi}{3})= \frac{1}{2}$
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 5 - Section 5.5 - Inverse Trigonometric Functions and Their Graphs - 5.5 Exercises - Page 445: 45
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