Engineers tend to prefer using degrees (o) to radians (rad), if for no other
reason, they are more comfortable with degrees: 360 is easy to remember,
and easy to divide, being equal to 23⋅32⋅5.
The following are three arguments why you should use radians instead of degrees.
is measured in radians, then the derivative of sin(x) and cos(x) are
cos(x) and -sin(x), respectively.
If x is measured in degrees, then the derivatives of
sin(x) and cos(x) are
180/π cos(x) and -180/π sin(x), respectively.
If x is measured in radians, then:
- sin(x) ≈ x
- cos(x) ≈ 1 - ½ x2
- tan(x) ≈ x
If x is measured in radians, the formulae require appropriate constant
Complex Exponential Function
The expanded version of the exponential function when using a complex
exponent is of the form:
where the arguments of sin and cos are measured in radians.
As for the comment that radians are too difficult to learn:
The Canadian army uses radians, or a good approximation thereunto. The
mil is defined such that there are 6400 mils to a circle, and therefore
one mil is a good approximation to one milliradian (mrad) (with a relative
error of less than 2%). Soldiers actually use the approximation tan(x) ≈ x
when they use the fact that an error of n mils when calculating a bearing
results in an error of n m at a distance of 1 km (1 km · tan(0.001 n) ≈ 0.001n km = n m).
If infantry soldiers can learn to use (and love)
radians (even if they don't know it) then an engineer can, too.