Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics

11252019, 06:56 AM
Post: #2




RE: Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics
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. 

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Messages In This Thread 
Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics  jklsadf  11252019, 06:40 AM
RE: Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics  jklsadf  11252019 06:56 AM
RE: Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics  Albert Chan  11252019, 04:32 PM
RE: Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics  Albert Chan  11272019, 06:31 PM
RE: Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics  jklsadf  11262019, 01:02 AM
RE: Arcsin in Valentin Albillo's HP12C Tried & Tricky Trigonometrics  Don Shepherd  11262019, 03:33 AM

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