Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.3 - Solving Trigonometric Equations - 7.3 Exercises - Page 531: 67


$x=arccos\frac{1}{4}+2n\pi$, where $n$ is an integer.

Work Step by Step

$sec^2x-4~sec~x=0$ $sec~x(sec~x-4)=0$ $sec~x=0$. But, there is no $x$ such that $sec~x=0$. $sec~x-4=0$ $sec~x=4$ $\frac{1}{cos~x}=4$ $cos~x=\frac{1}{4}$ $x=arccos\frac{1}{4}$ The period of $cos~x$ is $2\pi$. So, add multiples of $2\pi$ to each solution to find the general solution: $x=arccos\frac{1}{4}+2n\pi$, where $n$ is an integer.
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