Answer
$-\frac{\sqrt3}{2}$
Work Step by Step
RECALL:
Since sine and arcsine are inverse functions of each other, then, for all valid values of $x$,
$\sin{(\arcsin(x))}=x$
Thus,
$\sin{(\arcsin{(-\frac{\sqrt3}{2})})}=-\frac{\sqrt3}{2}$
Trigonometry (10th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
0321671775
ISBN 13:
978-0-32167-177-6
Chapter 6 - Review Exercises - Page 285: 24
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