The angle that marks the length of the radius on the circumference is 1 rad, i.e. the full angle is rad.
The radian (unit symbol: rad ) is an angular measure in which the angle is given by the length of the corresponding circular arc in the unit circle . Due to the consideration of the arc to indicate the angle of the reference "is in radians " also arc angle called. The arc length of a given angle is proportional to the radius . On a circle with a radius of 5 cm, an angle of 1 rad marks an arc of 5 cm. The full circle (360 °) has the arc length , so the full angle is rad.
Scientific pocket calculators calculate angle functions either in degrees or in radians, sometimes also in gons , where the full angle is 400 gon. The calculation modes on most pocket calculators are called "DEG" (from English degree for degree) for the degree, "RAD" for the radian measure and "GRA" or "GRAD" for the gon angle, and can sometimes be accessed via a combination key " DRG “(from the first letters of the units) switchable.
Trigonometric functions in mathematical libraries for programming languages and in programs for spreadsheets usually use the radian measure, and degrees therefore usually have to be converted. The full angle is 2 radians or 360 degrees , therefore:
So the factor for converting radians to degrees is
In the SI, it was initially left open whether radians and steradian are derived units or base units; the class of “complementary units” was created for both. In 1980 the CIPM recommended that these supplementary units be interpreted as derived. This was followed in 1995 by the 20th CGPM and resolved in resolution 8 to abolish the class of supplementary units.