Question

An angle of 1.5 rad intercepts an are on the unit circle. What is the length of the intercepted arc?

Answer 1

The arc length is related to the angle and length of the radius of the circle via the equation

$S=r\theta$

This is a unit circle, hence, r = 1. The angle is given as 1.5 radians or can be written as 1.5π. Hence, the length of the intercepted arc is computed as

$\begin{gathered} S=(1)(1.5\pi) \\ S=1.5\pi \end{gathered}$