Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.4 - Arc Length and Area of a Sector - 3.4 Problem Set - Page 153: 12


$\frac{4\pi}{3}\approx4.19$ mm

Work Step by Step

We know that the length of the arc $s$ cut off by $\theta$ can be calculated as $s=r\theta$. We are given that $\theta=60^{\circ}$ and $r=4$ mm. To convert $\theta$ to radians, we must multiply $\theta$ by $\frac{\pi}{180}$. $\theta=60^{\circ}=60(\frac{\pi}{180})=\frac{60\pi}{180}=\frac{\pi}{3}$ Therefore, $s=\frac{\pi}{3}(4)=\frac{\pi}{3}\times4=\frac{\pi\times4}{3}=\frac{4\pi}{3}\approx4.19$ mm.
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