Question

use the information in the diagram to determine the radian measure of the angle $varphi$.

Explanation:

Step1: Recall angle - radian relationship

The full - circle has an angle of $2\pi$ radians. The angle $\varphi$ in the diagram is a full - circle plus a half - circle.

Step2: Calculate the radian measure

A full - circle is $2\pi$ radians and a half - circle is $\pi$ radians. So, $\varphi=2\pi+\pi$.
$\varphi = 3\pi$ radians.

Answer:

$3\pi$