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.

# 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 x2
• 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.