Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 109: 77

Answer

$r=\frac{L}{\theta}$

Work Step by Step

Since the figure containing $L$, $r$ and $\theta$ represents a sector of a circle, $L$ is therefore equal to the arc length. The general formula for arc length $s$ of a sector of a circle is $s=r\theta$. Since $L$ is equal to $s$, this formula can be written as $L=r\theta$. Solving for $r$, the formula becomes $r=\frac{L}{\theta}$.
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