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: 85

Answer

(a) $3\pi\ rad$ (b) $24\pi\ in$ (c) $\frac{8\pi}{3}\ in/min$

Work Step by Step

Given $r=8\ in, \omega=\frac{\pi}{3}\ rad/min, t=9\ min$, we have: (a) the angle generated by P in time t is $\theta=\omega t=\frac{\pi}{3}\times9=3\pi\ rad$ (b) the distance traveled by P along the circle in time t is $s=r\theta=24\pi\ in$ (c) the linear speed of P is $v=\omega r=\frac{\pi}{3}\times8=\frac{8\pi}{3}\ in/min$
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