Radians and Degrees
Radians and Degrees
Radians are another way to measure angles. Sometimes radians will be used in questions, and other times you may choose to use them since they are sometimes more convenient than degrees.
A degree is equal to 1 /360 of a circle, while a radian is equal to the angle that intercepts an arc of the same length as the radius of the circle. In the figure below, arc AB has length r, and the central angle measures one radian.
When converting between the two measurement systems, use the proportion:
which can be simplified to:
To convert from degrees to radians:
multiply the degree measure by π /180. For example, 60º is equal to 60π/ 180 = π /3 radians.
To convert from radians to degrees:
multiply the measure in radians by 180 /π. For example, π/4 radians is equal to 180π/ = 45º.
Here are the most important angle measures in degrees and radians:
On the Math IC, it is sometimes a better idea to work solely in radians, rather than convert back and forth between radians and degrees. Using radians is especially easy on graphing calculators that allow you to switch into radian mode.
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