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: 106


The exact value of the provided expression is $\frac{4}{5}$.

Work Step by Step

Let us assume $\theta ={{\cos }^{-1}}\left( \frac{3}{5} \right)$. Then, $\cos \theta =\frac{3}{5}$ As $\cos \theta $ is positive, $\theta $ lies in the first quadrant. Now, by using the Pythagorean theorem: $\begin{align} & {{r}^{2}}={{x}^{2}}+{{y}^{2}} \\ & {{5}^{2}}={{3}^{2}}+{{y}^{2}} \\ & y=\sqrt{25-9} \\ & y=4 \end{align}$ Then, the value of the given expression is $\begin{align} & \sin \left[ {{\cos }^{-1}}\frac{3}{5} \right]=\sin \theta \\ & =\frac{y}{r} \\ & =\frac{4}{5} \end{align}$
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