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Radian


Radian

The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1.

A full angle is therefore 2pi radians, so there are 360 degrees per 2pi radians, equal to 180 degrees/pi or 57.29577951 degrees/radian. Similarly, a right angle is pi/2 radians and a straight angle is pi radians.

Radians are the most useful angular measure in calculus because they allow derivative and integral identities to be written in simple terms, e.g.,

 d/(dx)sinx=cosx

for x measured in radians.

Unless stated otherwise, all angular quantities considered in this work are assumed to be specified in radians.


See also

Angle, Arc Minute, Arc Second, Degree, Gradian, Steradian

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Cite this as:

Weisstein, Eric W. "Radian." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Radian.html

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