The answer involves the best way to define the function sin x...which turns out to be by measuring x in radians.
To get the full answer you should consult a textbook of calculus...I recommend "Calculus" by M. Spivak.
A slightly simpler but less responsive answer is because the derivatives (and, in fact, everything else about the trig functions) work out more easily if you measure in radians. But again, you need to read much more than my answer to get the full story.
