Radian
The radian is the SI derived unit of angle. It is defined as the angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle.
An angle measuring 1 radian subtends an arc equal in length to the radius of the circle
There are 2&pi (about 6.283185) radians in a complete circle, so:
2π rad = 360°
1 rad = 360/(2π)° = 180/π° (approximately 57.29578ð).
or:
360° = 2π rad
1° = 2π/360 rad = π/180 rad
In calculus, angles must be represented in radians in trigonometric functions, to make identities and results as simple and natural as possible. For example, the use of radians leads to the simple identity
The radian was formerly an SI supplementary unit, but this category was abolished from the SI system in 1995.
For measuring solid angles, see steradian.