Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 273: 2

Answer

The corresponding values of $x$ are $$\{\frac{\pi}{8}, \frac{5\pi}{6}, \frac{5\pi}{4}\}$$

Work Step by Step

1) The question asks for solutions over the interval $[0,2\pi)$, meaning that $$x\in[0,2\pi)$$ or $$0\le x\lt2\pi$$ 2) Now from also the question, your work leads to $$\frac{1}{2}x=\frac{\pi}{16}, \frac{5\pi}{12}, \frac{5\pi}{8}$$ To find corresponding values of $x$ from $\frac{1}{2}x$, we multiply both sides by $2$ $$x=\frac{\pi}{8}, \frac{5\pi}{6}, \frac{5\pi}{4}$$ 3) Finally, it is crucial to compare the values of $x$ in 2) with the range found in 1). We see that all three values of $x=\frac{\pi}{8}, \frac{5\pi}{6}, \frac{5\pi}{4}$ fit in the range of $x\in[0,2\pi)$. None would be eliminated as a result. The corresponding values of $x$ are $$\{\frac{\pi}{8}, \frac{5\pi}{6}, \frac{5\pi}{4}\}$$
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