Why finding the derivative of trig functions, why must the angle be in radians?why not degrees?
It comes from the derivation of the derivative of sin x.
Let
Then
(I won't prove this identity; uses the fact that sin(a+b) - sin(a-b) = 2 sin(b) cos (a), and then let x + h = a + b, x = a - b, solve for a and b and plug into above formula)
The derivative limit definition then is
The cosine term can be moved out by continuity of the cosine function. This gives
It can be proved, using a geometric argument comparing the area of an inscribed triangle with the corresponding sector and a tangential triangle, that the final limit is 1 if and only if h is measured in radians. If it's measured in degrees, you'll need a conversion factor here.