Question

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

Explanation:

Step1: Recall angle - radian relationship

In a unit - circle, a full - circle rotation is \(2\pi\) radians. The angle \(\varphi\) in the diagram is a quarter - circle rotation in the clockwise direction.

Step2: Calculate the radian measure

Since a quarter - circle rotation has an angle measure of \(\frac{1}{4}\) of a full - circle rotation and a full - circle is \(2\pi\) radians, and it is in the clockwise direction (negative), the radian measure of \(\varphi=-\frac{2\pi}{4}=-\frac{\pi}{2}\).

Answer:

\(-\frac{\pi}{2}\)