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A radian is a value without a dimension, so actually just a number. However, trigonometric functions only work well if you use radians.



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


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