Radial Based Approximations for Arcsine, Arccosine, Arctangent and Applications

Based on the geometry of a radial function, sequence approximations for arcsine, arccosine and arctangent are detailed. The arcsine sharp at points zero one. Convergence is proved convergence significantly better than Taylor series arguments approaching established can be utilized as basis Newton-Raphson iteration analytical approximations, modest complexity, with relative error bounds order 10−16, lower, defined. Applications include: first, upper lower bounded functions, arbitrary accuracy, arctangent. Second, higher accuracy based or approximations. Third, square well this function. Fourth, to even powers, errors that published Fifth, inverse tangent integral function several unknown integrals.