## Trigonometry 7th Edition

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