Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.5 - More Trigonometric Equations - 7.5 Exercises: 40

Answer

$\frac{\pi}{3}$, $\frac{5\pi}{3}$

Work Step by Step

$\cos \theta\cos 2\theta+\sin \theta\sin 2\theta=\frac{1}{2}$ $\cos (\theta-2\theta)=\frac{1}{2}$ $\cos (-\theta)=\frac{1}{2}$ Since cosine is an even function, $\cos \theta=\frac{1}{2}$. The only solutions in $[0, 2\pi)$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.
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