sin x = x - (x^3 / 3!) + (x^5 / 5!) - (x^7 / 7!) + ... =
= sum ( (-1)^n * (x ^ (2n+1) ) / (2n + 1)! )
Processors should be able to count sine, even in virtual machine.
In processor some values should be precalculated for speed.
There can be even dynamic cache used. It means that most popular values will remain. Along with some predetermined (strategic).