Question

Find the length of the arc on the unit circle with the given central angles 240º

Answer 1

The length of the arc is

$s=r\theta$

where $r$ is the radius and $\theta$ is the central angle, in radians.

$240\degree=\frac{240}{180}\pi=\frac{4\pi}{3}$ radians

The radius of the unit circle is 1.

$s=1\cdot\frac{4\pi}{3}=\frac{4\pi}{3}$

Answer: the length of the arc on the unit circle with the central angle of $240\degree$ is $\frac{4\pi}{3}$ units.