Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.2 The Unit Circle and Circular Functions - 6.2 Exercises - Page 589: 68


$1.3634$ radians

Work Step by Step

RECALL: $\csc{\theta}=\dfrac{1}{\sin{\theta}}$ and $\sin{\theta}=\dfrac{1}{\csc{\theta}}$ With $\csc{s}=1.0219$, then $\sin{s}=\dfrac{1}{1.0219}$ To find $s$, use the inverse sine function of a calculator in radian mode, then round-off the answer to four decimal places to obtain: $s=\sin^{-1}{(\frac{1}{1.0219})} \approx 1.3634$ The angle must be within the interval $[0, \frac{\pi}{2}]$, Noe that $\frac{\pi}{2}\approx 1.5708$. Thus, the $s-1.3634$ is within the required interval.
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