Practice Radians in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A radian measures angle by arc length: one radian subtends an arc equal to the circle radius.

It ties angle directly to the circle’s geometry instead of degree counting.

Example 1

easy
Convert 150Β° to radians.

Example 2

medium
Find the arc length of a sector with radius 10 cm and central angle \frac{3\pi}{4} radians.

Example 3

medium
Convert \frac{7\pi}{4} radians to degrees and identify which quadrant this angle is in.

Example 4

hard
A wheel of radius 30 cm rotates at 120 rpm (revolutions per minute). Find the angular velocity in radians per second and the linear speed of a point on the rim.