Practice Radians in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A radian is an angle measurement defined by the arc length it subtends on a unit circle: one radian is the angle at which the arc length equals the radius. A full circle is radians (about 6.28 radians), making radians the natural unit for trigonometry and calculus.
It ties angle directly to the circle’s geometry instead of degree counting.
Showing a random 20 of 50 problems.
Example 1
mediumConvert radians to degrees.
Example 2
challengeShow that for small in radians, . Use it to estimate .
Example 3
hardFind the area of a sector with radius cm and arc length cm.
Example 4
easyConvert to radians.
Example 5
mediumA central angle of radians subtends an arc of length cm. What is the radius?
Example 6
easyConvert radians to degrees.
Example 7
easyIn a unit circle, what arc length is subtended by an angle of radians?
Example 8
easyApproximately how many degrees is radian?
Example 9
challengeOn a circle of radius , an inscribed angle subtends an arc of length . Find the inscribed angle in radians.
Example 10
mediumA pendulum swings through an arc of m on a string of length m. Find the angle swept in radians.
Example 11
hardCompute the linear speed at the equator due to Earth's rotation if Earth's radius is km and it rotates once every hours.
Example 12
hardFind .
Example 13
easyConvert to radians.
Example 14
mediumConvert radians to degrees and identify which quadrant this angle is in.
Example 15
mediumFind the area of a sector with radius and central angle .
Example 16
hardA wheel of radius cm rotates at rpm (revolutions per minute). Find the angular velocity in radians per second and the linear speed of a point on the rim.
Example 17
mediumExpress as a positive coterminal angle in .
Example 18
easyConvert radians to degrees.
Example 19
easyConvert to radians.
Example 20
mediumA wheel turns through radians. How many full revolutions is that?