Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.4 Trigonometric Functions and Their Inverse - 1.4 Exercises - Page 48: 40


$\boxed{\theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}}$

Work Step by Step

$cos^2(\theta) = \frac{1}{2}$, which means $cos(\theta) = +\frac{\sqrt{2}}{2}$ or $cos(\theta) = -\frac{\sqrt{2}}{2}$ For the first case, $cos(\theta) = +\frac{\sqrt{2}}{2}$, $\theta = \frac{\pi}{4}, \frac{7\pi}{4}$. For the second case, $cos(\theta) = -\frac{\sqrt{2}}{2}$, $\theta = \frac{3\pi}{4}, \frac{5\pi}{4}$. Overall, the solutions for $\theta$ are: $\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$.
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