Radian
A radian is a value without a dimension, so actually just a number. However, trigonometric functions only work well if you use radians.
Explanation
In particular, only sines and cosines that map radians to ratios satisfy the differential equation.
Example 1
If an argument to sine is scaled by a frequency x, like in
then the first derivative gives
The second derivative shows
If this same sine is expressed in radians you get a different solution