Radian measure

Radians are a unit of measurement for angles. They are natural in that they are pure numbers. The radian measure of an angle is the length of arc subtended by the angle divided by the radius.

Since a whole circle (360°) has an arc length of 2πr, it must be 2π radians. So
1° = π/180 radians and
1 radian = 180/π = 57.29577951 °.

The radian is the natural argument for the trigonometric functions. Unless otherwise stated, in maths sin x always refers to the sine of x radians. Calculators usually have two modes, either degree mode or radian mode.

The length of arc of a circle of angle θ radians is easily stated -mathformula2 not MarkupType-
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