Question

arc cd is $\frac{2}{3}$ of the circumference of a circle. what is the radian measure of the central angle?
$\frac{2\pi}{3}$ radians
$\frac{3\pi}{4}$ radians
$\frac{4\pi}{3}$ radians
$\frac{3\pi}{2}$ radians

Explanation:

Step1: Recall the formula for radian measure

The radian measure of a full - circle is \(2\pi\) radians.

Step2: Calculate the radian measure of the central angle

If arc \(CD\) is \(\frac{2}{3}\) of the circumference, then the radian measure of the central angle \(\theta\) is \(\theta=\frac{2}{3}\times2\pi\).

$$
LATEXBLOCK0
$$

Answer:

\(\frac{4\pi}{3}\) radians (the third option)