[EricVanWyk]

Originally Posted by Ether

Taylor expansion is not the best tool to use for this purpose.

See the discussion about ATAN2 nonlinear model fitting here:

http://www.chiefdelphi.com/media/papers/2390

I spent the summer porting a fixed point math library to Arm's Thumb2 assembly, and learned a lot when I hit the arc-trig functions. At the high school level, suffice it to say that these functions are very-not-polynomials and therefore hate Taylor series expansions. At the college level, suffice it to say that if I ever teach numerical approximations the final exam will be to approximate arcsine.