[drinkwell]

Because with a Fourier series/transform you only get to play with the amplitude of the sine and cosine functions, not the offset. If you only had cosine functions in your sum you'd only be able to represent symmetric functions (and antisymmetric if only sine). Except actually I lied; if you sum both sine and cosine functions you do get to specify offsets. Think of this trig identity: sin(x + offset) = [cos(offset)] sin(x) + [sin(offset)] cos(x). Think about the terms in brackets as just being amplitudes. By having both sine and cosine in the sum you can represent any arbitrary offset by just changing their relative amplitude. This is one of those things which is nicer when you think about it in terms of complex numbers.