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 2^{3}⋅3^{2}⋅5.

The following are three arguments why you should use radians instead of degrees.

# Derivatives

If *x*
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.

# Approximations

If *x* is measured in radians, then:

- sin(
*x*) ≈ *x*
- cos(
*x*) ≈ 1 - ½ *x*^{2}
- tan(
*x*) ≈ *x*

If *x* is measured in radians, the formulae require appropriate constant
multipliers.

# 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.

# Milliradians (mils)

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*) ≈ 0.001*n* 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.