Question

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

Explanation:

Step1: Recall full circle radians

A full circle has $2\pi$ radians.

Step2: Calculate 1/4 of full circle

Multiply total radians by $\frac{1}{4}$:
$\frac{1}{4} \times 2\pi = \frac{\pi}{2}$

Answer:

$\frac{\pi}{2}$ radians