Question

arc cd is $\frac{1}{4}$ of the circumference of a circle. what is the radian measure of the central angle?
$\frac{\pi}{4}$ radians
$\frac{\pi}{2}$ radians
$2\pi$ radians
$4\pi$ radians

Explanation:

Step1: Recall the total radians in a circle

The total radians in a circle is \(2\pi\).

Step2: Calculate the radian measure of the central angle

Since arc \(CD\) is \(\frac{1}{4}\) of the circumference, the central angle \(\theta=\frac{1}{4}\times2\pi\).

$$ \theta = \frac{2\pi}{4}=\frac{\pi}{2} $$

Answer:

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