So Thomas Z.,
You COULD just write your Taylor series expansions for sin and cos and start cranking! sin = x - x^3/3! etc. and cos = 1 - x^2/2! etc.., look 'em up. Or you COULD be way smarter and employ your trig identity sin(x)*cos(x)=(1/2)sin(2x). Which way do you think would be faster?
-- Cheers, --Mr. d.