Question

arc ab is $\frac{1}{3}$ of the circumference of a circle. what is the radian measure of the central angle? 3$pi$ radians $\frac{pi}{3}$ radians $\frac{2pi}{3}$ radians $\frac{3pi}{2}$ radians

Explanation:

Step1: Recall the total radian measure of a circle

The total radian measure of a full - circle is $2\pi$ radians.

Step2: Calculate the central angle

Since arc AB is $\frac{1}{3}$ of the circumference of the circle, the central angle corresponding to arc AB is $\frac{1}{3}$ of the total radian measure of the circle. So the central angle $\theta=\frac{1}{3}\times2\pi=\frac{2\pi}{3}$ radians.

Answer:

$\frac{2\pi}{3}$ radians