Precalculus (6th Edition) Blitzer

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

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 46


$$x=0, \qquad x=\pi$$

Work Step by Step

We solve by factoring: $$\cos ^2 \theta -1=0 \quad \Rightarrow \quad \cos ^2 \theta =1 \quad \Rightarrow \quad \cos \theta = \pm 1 \quad \Rightarrow \quad x= 2n\pi, \quad \text{ or } \quad x=\pi + 2n \pi, \quad n \in \mathbb{Z}$$So, $x= 0$ and $x= \pi$ are the only solutions in the interval $[0, 2\pi )$.
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