Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 279: 13


The corresponding values of $x$ are $$\{\frac{\pi}{3}, \pi, \frac{4\pi}{3}\}$$

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 your work leads to $$2x=\frac{2\pi}{3}, 2\pi, \frac{8\pi}{3}$$ To find corresponding values of $x$ from $2x$, we divide both sides by $2$ $$x=\frac{\pi}{3}, \pi, \frac{4\pi}{3}$$ 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 $x=\frac{\pi}{3}, \pi, \frac{4\pi}{3}$ fit in the range of $x\in[0,2\pi)$. None would be eliminated as a result. The corresponding values of $x$ are $$\{\frac{\pi}{3}, \pi, \frac{4\pi}{3}\}$$
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