Precalculus (6th Edition) Blitzer

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

Chapter 4 - Review Exercises - Page 646: 101


The exact value of the provided expression is $1$.

Work Step by Step

Let us assume $\theta ={{\cos }^{-1}}\left( 0 \right)$. Then, we have $\cos \theta =0$ We know that for the cosine function, the interval for the angle is $\left[ 0,\pi \right]$. Therefore, the only angle that satisfies $\cos \theta =0$ is $\frac{\pi }{2}$. Hence, $\theta =\left( \frac{\pi }{2} \right)$ and the exact value of the given expression is $\begin{align} & \sin \left( {{\cos }^{-1}}0 \right)=\sin \left( \theta \right) \\ & =\sin \left( \frac{\pi }{2} \right) \\ & =1 \end{align}$
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