Here is the short note about derivatives. Radians and Derivatives
Also, here is how to think of radians. (due to my wife)
I told her that if you don’t use radians, the derivative of the sin is a constant (not equal to one) times the cosine. She thought about it and told me that this is how she saw it.
Take a slinky and attach a stick to it at the place where the slope is the greatest. Then stretch it until the stick is at 45 degrees. The scale on the horizontal axis will be the scale that you need to use for the derivative of the sine to be the cosine.
I hope that is clear.