Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.3 Trigonometric Equations - 7.3 Assess Your Understanding - Page 466: 11


$2.42, 3.86$.

Work Step by Step

The domain of $\cos^{-1}{x}$ is the range of $\cos{x}$, which is $[−1, 1] $. The range of $\cos^{-1}{x}$ is a specified domain of $\cos{x}$, i.e. $\left[0,\pi \right]$. This equation is the same as: $\cos(\theta)=-\frac{3}{4}$ because $4\cos(\theta)+3=0\\4\cos(\theta)=-3\\\cos(\theta)=-\frac{3}{4}$ After using a calculator in radian mode the solutions for $\cos^{-1}{-0.75}$ is $2.41$ (given by the calculator) and because the cosine function is symmetric to $x=\pi$ the second solution is: $\pi+(\pi-2.41)\approx3.86$. (for it to be in the right domain).
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