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Radian Measure of Angles

Radian measure sizes an angle by the arc length it subtends on a circle divided by that circle's radius, making the measure a pure ratio independent of circle size, with one full revolution equal to two pi radians. This gives a scale on which the unit circle's arc length and the angle itself are the same number, and provides the conversion to and from degrees. It is the angle unit used whenever angles are treated as inputs to functions plotted on a numerical axis in analytic geometry and mathematical physics.