See Radian (band) for the Austrian trio.
1 rad = m·m–1 = 1
The radian is useful to distinguish between quantities of different nature but the same dimension. For example angular velocity can be measured in radians per second (rad/s). Retaining the word radian emphasizes that angular velocity is equal to 2π times the rotational frequency.
In practice, the symbol rad is used where appropriate, but the derived unit "1" is generally omitted in combination with a numerical value.
The angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle is one radian. Angle measures in radians are often given without any explicit unit. When a unit is given, sometimes the abbreviation rad is used, sometimes the symbol c (for "circular"). Care must be taken with this symbol since it can be mistaken for the ° (degree) symbol.
There are 2π (approximately 6.28318531) radians in a complete circle, so:
More generally, we can say:
If, for example, -1,570796 in radians was given, the corresponding degree value would be:
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 other elegant identities in mathematics, including
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 distances is dimensionless.
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.
bg:Радиан ca:Radiant (angle) cs:Radián da:Radian de:Bogenmaß et:Radiaan es:Radián fr:Radian gl:Radián ko:라디안 it:Radiante he:רדיאן nl:Radiaal ja:ラジアン no:Radian pl:Radian pt:Radiano ru:Радиан sl:Radian sr:Радијан fi:Radiaani sv:Radian uk:Радіан