Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises: 64

Answer

$-\displaystyle \frac{\sqrt{3}}{2}$

Work Step by Step

Letting $A=2\displaystyle \theta, \quad \cos A=\frac{1}{2}$ we express $\displaystyle \theta=\frac{A}{2},\quad\cos\theta=\cos\frac{A}{2}$ ($\cos\theta$ is negative as $\theta$ terminates in Q.II.) Half-Angle identity: $\cos\theta$=$\displaystyle \cos\frac{A}{2}=-\sqrt{\frac{1+\cos A}{2}}=-\sqrt{\frac{1+\frac{1}{2}}{2}}$ $=-\displaystyle \sqrt{\frac{3}{4}}=-\frac{\sqrt{3}}{2}$
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