Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Review Exercises - Page 708: 41


$\frac{\sqrt {2-\sqrt 2}}{2}$

Work Step by Step

Use the half-angle formula $sin\frac{u}{2}=\pm\sqrt {\frac{1-cos(u)}{2}}$; for $\frac{u}{2}=22.5, u=45$, choose the positive sign to get $sin22.5=\sqrt {\frac{1-cos(45)}{2}}=\sqrt {\frac{1-\sqrt 2/2}{2}}=\frac{\sqrt {2-\sqrt 2}}{2}$
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