Arctangent function program [HP-42S, Free42]

[Gerson W. Barbosa]

(09-19-2024 04:25 AM)Thomas Klemm Wrote:  Example

1 R/S

y: 0.8414709848078965065362209309116153
x: 0.54030230586813971758203414358187

÷

x: 1.557407724654902229769750316481308

With the patched HP-12C program above I get

1 ENTER 47 R/S ; RAD mode
R/S ->

HP-12C:

Z: 1.557407724
Y: 0.5403023061
X: 0.8414709848

HP-12C Platinum:

Z: 1.557407725
Y: 0.5403023059
X: 0.8414709848

I had made some tests using the tangent half-angle formula in the second half of the first quadrant. That would need six instead of eleven iterations, but I don’t think it’s worth the additional steps since current 12C calculators are extremely fast.
The program loses accuracy near critical points like 90° and 180°, so it’s meant for everyday trigs only.
Anyway, when maximum accuracy is needed this program should be used instead (HP-12C Platinum only). Because of page width change, my formatting has been completely ruined. That is the same program in the old article forum, except for the one-step reduction to make the ATAN entry-point more consistent with the ones for ACOS and ASIN.