Trigonometry (11th Edition) Clone

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

Chapter 6 - Review Exercises - Page 291: 39


$\left\{\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}\right\}$

Work Step by Step

Note that the values of the tangent and tangent functions are equal when $x=\frac{\pi}{4},$ $(\tan{\frac{\pi}{4}}=\cot{\frac{\pi}{4}}=1)$ and when $-\frac{\pi}{4},$ $(\tan{(-\frac{\pi}{4})}=\cot{(-\frac{\pi}{4})}=-1$. Since the period of these functions is $\pi$, then the tangent and cotangent of $\frac{\pi}{4} + \pi=\frac{5\pi}{4}$, $-\frac{\pi}{4}+\pi = \frac{3\pi}{4}$, and $\frac{3\pi}{4}=\pi=\frac{7\pi}{4}$, are also equal. Therefore, the solutions to the given equation that are within the interval $[0, 2\pi)$, are $\frac{\pi}{4}, \frac{3\pi}{4},$ and $\frac{5\pi}{4}$.
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