Answer
$ -\frac{\sqrt {2-\sqrt 2}}{2}$
Work Step by Step
$sin(-\frac{\pi}{8})=-sin(\frac{\pi}{8})=-\sqrt {\frac{1-cos(\frac{\pi}{4})}{2}}=-\sqrt {\frac{1-\frac{\sqrt 2}{2}}{2}}=-\frac{\sqrt {2-\sqrt 2}}{2}$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 497: 29
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