Here are definitions of the basic trigonometric functions alternative to the Taylor series. They use complex numbers and Euler's formula. By the way, could someone tell me how to make my code stand out in a comment? Thanks.
(= e 2.71828182845904523539)
(= pi 3.14159265358979323846)
(def sin (x)
(/ (- (expt e (* 0+1.i x)) (expt e (* 0-1.i x))) 0+2i))
(def cos (x)
(/ (+ (expt e (* 0+1.i x)) (expt e (* 0-1.i x))) 2.0))