Practice Radian Measure in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An angle measure defined by the arc length subtended on a unit circle: one radian is the angle that subtends an arc equal in length to the radius.
Imagine wrapping the radius of a circle along its edge like a piece of string. The angle you've swept out is exactly 1 radian. Since the full circumference is 2\pi r, a full turn is 2\pi radians. Radians measure angles in terms of the circle itself, which is why they're the natural unit for calculus and physicsβno arbitrary conversion factor like 360 is needed.
Example 1
easyConvert 135Β° to radians and \dfrac{5\pi}{6} radians to degrees. Show the conversion steps.
Example 2
mediumA wheel of radius 5 cm rotates through an angle of 2.4 radians. Find the arc length and the area of the sector swept.
Example 3
easyConvert: (a) 60Β° to radians, (b) 270Β° to radians, (c) \dfrac{\pi}{3} to degrees, (d) \dfrac{7\pi}{6} to degrees.
Example 4
mediumA clock's minute hand is 15 cm long. How far does its tip travel in 20 minutes? How large is the sector area swept?