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: 26


The solution set is $$\{0,\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{7\pi}{4}\}$$

Work Step by Step

$$\tan4x=0$$ over interval $[0,2\pi)$ 1) Find corresponding interval for $4x$ Interval $[0,2\pi)$ can be written as $$0\le x\lt2\pi$$ That means, for $4x$, the interval would be $$0\le4x\lt8\pi$$ or $$4x\in[0,8\pi)$$ 2) Now consider back the equation $$\tan4x=0$$ Over the interval $[0,8\pi)$, there are 8 values whose $\tan$ equals $0$, which are $0,\pi,2\pi,3\pi,4\pi,5\pi,6\pi,7\pi$, meaning that $$4x=\{0,\pi,2\pi,3\pi,4\pi,5\pi,6\pi,7\pi\}$$ So $$x=\{0,\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{7\pi}{4}\}$$
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