Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 6 - Section 6.3 - Trigonometric Equations Involving Multiple Angles - 6.3 Problem Set - Page 340: 35


$$x= \frac{ \pi}{8}+ \frac{ k\pi}{2} \ \text{or}\ x= \frac{3 \pi}{8}+ \frac{ k\pi}{2}$$

Work Step by Step

Given $$ \sin^2 4x = 1 $$ Then $$ \sin 4x =\pm 1 $$ We have two cases for $\sin 4x$ Case 1 $$\sin 4x=1$$ Then $$ 4x=\frac{ \pi}{2}+2k\pi \ \Rightarrow x= \frac{ \pi}{8}+ \frac{ k\pi}{2}$$ Case 2 $$\sin 4x=-1$$ Then $$ 4x=\frac{3 \pi}{2}+2k\pi \ \Rightarrow x= \frac{3 \pi}{8}+ \frac{ k\pi}{2}$$
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