Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.1 Angles and Their Measures - 5.1 Assess Your Understanding - Page 387: 92


$13.96 \text{ inches}$

Work Step by Step

Arc length $s$ can be computed using the formula $s=r\theta$ where $r$ is the radius of the circle and $\theta$ is the central angle. Here we have: $\theta=20^{\circ}=20\times\frac{\pi}{180}\,rad=\frac{\pi}{9}\,rad$ $r=40\,inches$ Using the formula for arclength gives: $s=40\text{ inches}\times\frac{\pi}{9}\approx 13.96 \text{ inches}$ Thus, the tip of the pendulum moves $13.96$ inches each second.
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