Since the trigonometric functions in java.lang.Math are quite slow: is there a library that does a quick and good approximation? It seems possible to do a calculation severa
Check out Apache Commons Math package if you want to use existing stuff.
If performance is really of the essence, then you can go about implementing these functions yourself using standard math methods - Taylor/Maclaurin series', specifically.
For example, here are several Taylor series expansions that might be useful (taken from wikipedia):


