Why Choose Radians Over Degrees for Measuring Angles?

[rollcast]

What are the advantages to using one system to measure an angle over another. For example why do we measure angular velocity in radians instead of degrees?

Are there any intrinsic advantages to one unit over another?

Thanks
AL

 

[Rajini]

Hi,
It is small/simple/compact to write ∏ than writing 180 degree.
Rajini.

 

[Integral]

Radians, being a ratio of 2 lengths, are unitless. They can be used as a pure number so a easier to compute with. One frequent application is in doing small angle approximations. Sin(x) = x for x small as long as x is in radians.

 

[mathman]

A major advantage is in calculus. The derivative of sin(x) is cos(x) as long as x is in radians.