Question

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

Explanation:

Step1: Observe the angle position

The angle $\varphi$ is a full - circle plus a quarter - circle in the clockwise direction. A full - circle in radians is $2\pi$ and a quarter - circle is $\frac{\pi}{2}$. Since it is clockwise, the angle is negative.

Step2: Calculate the radian measure

$\varphi=- (2\pi+\frac{\pi}{2})=-\frac{4\pi + \pi}{2}=-\frac{5\pi}{2}$

Answer:

$-\frac{5\pi}{2}$