Precalculus (6th Edition) Blitzer

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

Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 832: 58


The exact value is $\frac{5}{12}$.

Work Step by Step

Let us assume $\theta $ represents the angle. $\theta ={{\sin }^{-1}}\left( \frac{5}{13} \right)$ Then, $\sin \theta =\frac{5}{13}$ Since, $\sin \theta $ is positive, $\theta $ is in the first quadrant. Now, using the Pythagorean identity, we get $\begin{align} & {{x}^{2}}+{{y}^{2}}={{r}^{2}} \\ & {{x}^{2}}+{{5}^{2}}={{13}^{2}} \\ & {{x}^{2}}=169-25 \\ & x=12 \end{align}$ Thus, $\begin{align} & \tan \left( {{\sin }^{-1}}\left( \frac{5}{13} \right) \right)=\tan \theta \\ & =\frac{x}{y} \\ & =\frac{5}{12} \end{align}$
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