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: 85


The solution on the interval $[0,2\pi )$, correct to four decimal places, is $0.9695$ or $2.1720$.

Work Step by Step

We have to calculate the equation using a calculator; we keep the calculator in radian mode to find the inverse sine of $0.8246$. $\theta =\text{si}{{\text{n}}^{-1}}0.8246\approx 0.9695.$ Therefore, the sine is positive in quadrants I and II, thus, $x\approx 0.9695\ $ or $x\approx \pi -0.9695.$ And the value of $\pi $ is 3.14159. Hence, the value of $x$ is: $\begin{align} & x\approx 3.14159-0.8246 \\ & \approx 2.1720. \end{align}$
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