Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 130: 7


(a) $\theta = 1.57~rad$ (b) $d = 31.4~cm$ (c) $v = 5.24~cm/s$

Work Step by Step

(a) We can find the angle generated by P in time $t$: $\theta = \omega ~t$ $\theta = (\frac{\pi}{12}~rad/s)(6~s)$ $\theta = \frac{\pi}{2}~rad$ $\theta = 1.57~rad$ (b) We can find the distance $d$ traveled by P: $d = \theta ~r$ $d = (\frac{\pi}{2}~rad)(20~cm)$ $d = 10~\pi~cm$ $d = 31.4~cm$ (c) We can find the linear speed $v$ of P: $v = \frac{d}{t}$ $v = \frac{10~\pi~cm}{6~s}$ $v = \frac{5~\pi}{3}~cm/s$ $v = 5.24~cm/s$
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