Lesson: Chapter - 9

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.

To convert from degrees to radians:

multiply the degree measure by^p /₁₈₀. For example, 60º is equal to^60p/ ₁₈₀ = ^p /₃ radians.

To convert from radians to degrees:

multiply the measure in radians by ¹⁸⁰ /_p. For example, ^p/₄ radians is equal to ^180p/ _4p = 45º.

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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