Arcsin in Valentin Albillo's HP-12C Tried & Tricky Trigonometrics

[jklsadf]

After a little more googling, the initial scaling does seem to be using the half angle formula somehow sin(x/2) = +/- sqrt((1 - cos(x)) / 2). There was an additional square root on line 52 that gets applied to register 5 on all but the last iteration. The final multiplication by 8 is to undo this scaling.

The taylor series used is apparently that for arctan(x) = x - x^3/3 * x^5/5 - x^7/7 + ... which alternates signs for each term in the series, but I guess convergence is fine after the scaling. There must have been a change of variable to allow using the series for arctan, but I'm not sure how.