Radian

SI Supplementary Unit

The radian is the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius.

The circumference of a circle is defined as 2π*radius. Considering a unit circle centred on a Cartesian axis. By tracing the x-coordinate (starting at (x=1,y=0) and travelling counter-clockwise) versus arc length we obtain a Cosine wave and similary the y-coordinate yields a Sine wave. From this derives the definition that 360° equals 2π radians.

See also: Angles, Plane Angle, SI Units.