I was curious about that too. Gemini actually gave a decent list. Trig functions come from Euler's identity:

    e^ix = cos x + i sin x

which means:

    e^-ix = cos -x + i sin -x
          = cos x - i sin x

so adding them together:

   e^ix + e^-ix = 2 cos x
   cos x = (e*ix - e^-ix) / 2

So I guess the real part of that.

Multiplication, division, addition and subtraction are all straightforward. So are hyperbolic trig functions. All other trig functions can be derived as per above.