Home > Radian

There are 2 π (about 6.283185) radians in a complete circle, so:
2π rad = 360°
1 rad = 360/(2π)° = 180/π° (approximately 57.29578°).

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

which is the basis of many elegant identities in mathematics.

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.

1 Dimensional analysis

Although the radian is a unit of measure, anything measured in radians is dimensionless. This can be seen easily in that the ratio of an arc's length to its radius is the angle of the arc, measured in radians; yet the quotient of two distanceFor distance between people, see proxemics. Distance between two points The distance between two points is the length of a straight line between them. In the case of two locations on Earth, usually the distance along the surface is meant: either " as thes is dimensionless.

Another way to see the dimensionlessness of the radian is in the Taylor seriesIn mathematics, the Taylor series of an infinitely often differentiable real (or complex) function f defined on an open interval a − r a + r is the power series : Here, n is the factorial of n and f n a denotes the n''th derivative of f at the point for the trigonometric function :

If had units, then the sum would be meaningless; the linear term can not be added to the cubic term , etc. Therefore, must be dimensionless.

2 See also

• trigonometryTrigonometry (Greek: "the measure of triangles") is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine and cosine . It has some relationship to geometry, though there is disagreement on exactly what that relati
• harmonic analysisHarmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms. The basic waves are called "
• angular frequencyIn physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity . The term angular freque