# Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 130: 8

(a) $\theta = \frac{2\pi}{5}~rad$ which is $1.26~rad$ (b) $d = (12~\pi)~cm$ which is $37.7~cm$ (c) $v = (3~\pi)~cm/s$ which is $9.42~cm/s$

#### Work Step by Step

(a) We can find the angle generated by P in time $t$: $\theta = \omega ~t$ $\theta = (\frac{\pi}{10}~rad/s)(4~s)$ $\theta = \frac{2\pi}{5}~rad$ $\theta = 1.26~rad$ (b) We can find the distance $d$ traveled by P: $d = \theta ~r$ $d = (\frac{2\pi}{5}~rad)(30~cm)$ $d = 12~\pi~cm$ $d = 37.7~cm$ (c) We can find the linear speed $v$ of P: $v = \frac{d}{t}$ $v = \frac{12~\pi~cm}{4~s}$ $v = 3~\pi~cm/s$ $v = 9.42~cm/s$

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