Answer
$-\frac{\sqrt{2-\sqrt2}}{2}$
Work Step by Step
Using the given identities and the known values: $\sin (-22.5^\circ)=\pm\sqrt{\frac{1-\cos(-45^\circ)}{2}}=-\sqrt{\frac{1-(\frac{1}{\sqrt2})}{2}}=-\frac{\sqrt{2-\sqrt2}}{2}$
Algebra 2 (1st Edition)
by Larson, Ron; Boswell, Laurie; Kanold, Timothy D.; Stiff, Lee
Published by
McDougal Littell
ISBN 10:
0618595414
ISBN 13:
978-0-61859-541-9
Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Quiz for Lessons 14.6-14.7 - Page 962: 2
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