Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 88


The solution on the interval $[0,2\pi )$, correct to four decimal places, is $2.1790$ or $4.1041$.

Work Step by Step

We have to calculate the equation using a calculator in radian mode: $\theta ={{\cos }^{-1}}\frac{4}{7}\approx 0.9626$ And the cosine is negative in quadrants II and III, $x\approx \pi -0.9626$ And the value of $\pi $ is 3.14159. Thus, the value of $x$ is: $\begin{align} & x\approx 3.14159-0.9626 \\ & \approx 2.1790 \end{align}$ or $x\approx \pi +0.9626$ And the value of $\pi $ is 3.14159. Hence, the value of $x$ is: $\begin{align} & x\approx 3.14159+0.9626 \\ & \approx 4.1041 \end{align}$
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