Question

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

Explanation:

Step1: Recall the unit - circle concept

The angle $\varphi$ is measured counter - clockwise from the positive $x$ - axis. In a unit - circle, a full rotation is $2\pi$ radians.

Step2: Analyze the position of the angle

The angle $\varphi$ makes a half - rotation counter - clockwise. A half - rotation in radians is $\pi$ radians.

Answer:

$\pi$