Arcsin Approximation: General Recommendations

1. Taylor about the center of the interval is better than Taylor about another point.
2. Nothing can help Taylor if there's a nearby singularity.
3. Chebyshev is better than Taylor, and, altho not demonstrated here, it will still converge, albeit more slowly, even in the presence of nearby complex singularities.
4. Padifying a Taylor or Chebyshev will usually, but not always, improve it.
5. Minimax is, by definition, best, if it can be calculated.
6. It's good to use any special knowledge of the function, such as symmetry or removable singularities.
7. If more fast functions are available to use in the approximation, then a better approximation can be found.