Answer
$\frac{\sqrt{2+\sqrt2}}{2}$
Work Step by Step
Using the given identities and the known values: $\sin (5\pi/8)=\pm\sqrt{\frac{1-\cos(5\pi/4)}{2}}=\sqrt{\frac{1-(\frac{1}{\sqrt2})}{2}}=\frac{\sqrt{2+\sqrt2}}{2}$
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 - Guided Practice for Examples 1, 2, and 3 - Page 956: 2
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