Approximating inverse trigonometric functions

I have to implement asin, acos and atan in environment where I have only following math tools:

• sine
• cosine
• elementary fixed point arithmetic (floating point numbers are not available)

I also already have reasonably good square root function.

Can I use those to implement reasonably efficient inverse trigonometric functions?

I don't need too big precision (the floating point numbers have very limited precision anyways), basic approximation will do.

I'm already half decided to go with table lookup, but I would like to know if there is some neater option (that doesn't need several hundred lines of code just to implement basic math).

EDIT:

To clear things up: I need to run the function hundreds of times per frame at 35 frames per second.

Do you need a large precision for arcsin(x) function? If no you may calculate arcsin in N nodes, and keep values in memory. I suggest using line aproximation. if x = A*x_(N) + (1-A)*x_(N+1) then x = A*arcsin(x_(N)) + (1-A)*arcsin(x_(N+1)) where arcsin(x_(N)) is known.