yeah, sorry, just making fun of you
sin x can also be written as the sum over all ( (-1)^n x^(2n+1) / factorial(2n+1) ) for all n from 0 to infinity. here you can just take the first terms to have nice convergence around 0. the bigger your sum gets, the more precise it'll be. just check it out using excel or whatever ...
cos x is the same for ( (-1)^n x^(2n) / factorial(2n) )