Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.2 The Unit Circle and Circular Functions - 6.2 Exercises - Page 589: 86

Answer

(a) $40\pi\ rad$ (b) $480\pi\ ft$ (c) $96\pi\ ft/min$

Work Step by Step

Given $r=12\ ft, \omega=8\pi\ rad/min, t=5\ min$, we have: (a) the angle generated by P in time t is $\theta=\omega t=8\pi\times5=40\pi\ rad$ (b) the distance traveled by P along the circle in time t is $s=r\theta=480\pi\ ft$ (c) the linear speed of P is $v=\omega r=8\pi\times12=96\pi\ ft/min$
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