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Radians and Degrees

 

In science and engineering, radians are much more convenient (and common) than degrees. A radian is defined as the angle between 2 radii (radiuses) of a circle where the arc between them has length of one radius.

 

Another way of putting it is: a radian is the angle subtended by an arc of length r (the radius).

 

 

One radian is about 57.3°.

 

Radians are especially useful in calculus where we want to interchange angles and other quantities (e.g. length). For example, radians are required in Fourier Series - and other areas (see my numerical methods manuals).

Most computer programs use radians as the default.

The expression to convert degrees to radians is:  R= pi*D/180   where R is radians, D is degrees, and pi is 3.1416