Any maths buffs?

Didn't De moivre show that; Cos(x)^n = Re((Cos(x) + iSin(x))^n) = Re(e^ix)?
And similarly that Sin(x) was the Imaginary part of the above?

I don't think so. he only showed the first of your two equalities. Not the second, which is Euler.

http://en.wikipedia.org/wiki/De_Moivre's_formula (not gonna post this again: click it Tim!)