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

[Albert Chan]

(11-25-2019 06:56 AM)jklsadf Wrote:  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.

θ = asin(x)

After applying half-angle formula 3 times: θ/8 = asin(x') = atan(x' / √(1-x'²))