Trigonometrics on the 17bii+


Could someone point me to the recent, but obviously now archived, thread regarding this?

I believe there was a lot of discussion, initiated by Gerson, about applying his 12C trigonometry work to the 17bii+ equation solver, but I am darned if I can find it now....


Edited: 4 Mar 2007, 12:37 a.m.


Hi Les --

I believe it was either in "archv014" or "archv016". Take a look in each, and search for 17bii+. I was just reading them the other day, but unfortunately don't have the link with me.



Hi Les,

There's the Article by Bruce Maquire:

Improved TRIG. and INVERSE TRIG. functions for the HP-17BII

and the Message Thread started by Gerson Barbosa:

HP-17BII - trig equations suggestions

There may be others, but I think these are the main ones.



Hello Les,

There are five sets of equations you can use here:

I would suggest the first set, as it faster and easier to enter. This still can be improved by someone who knows the HP-17BII/II+ solver better, like placing SIN, COS and TAN into a single menu group. They have been tested on the HP-17BII. I am curious if they work on the HP-17BII+.

Best regards,



Hi Gerson,

How did I pick up on your message threads but totally miss your article? :) Sorry for missing it in my previous post.



Hi Bill,

I think it's my fault. In the last message in the thread Bill Platt suggested it went into the Articles. I should have provided a link to the article (or to the draft-article, as there is still room for improvement) while the thread was still active. Thanks for remembering it.



Edited: 4 Mar 2007, 7:37 a.m.


Hi Gerson. I entered the method 1 equations into a 17bii+ and all equations verify and solve within 2 seconds. I've tried a few values for x: 0, 15, 30, 45, 60, 75, and 90 and all seem to solve correctly. I'll do some more testing and will give you feedback.

Thanks for making this available to us.




Hello John,

If they verify and solve in less than two seconds, this means the 17BII+ is significantly faster than the 17BII, which is great! I was intending to group all six functions in a single menu but I quit because the verification time would be too slow.

I wasn't interested in giving a complete trigonometric solution on the HP-17BII when I suggested two simple polynomial equations for sine and arctangent functions. So it was really great when Charles presented basically the same equations I used in set one and showed that the inverse functions could be obtained iteratively, as you can see in the link provided by Bill. It was a good start.

Other values you can check:

  sin(18) = (sqrt(5) - 1)/4
cos(22.5) = (sqrt(2 + sqrt(2))/2
tan(72) = sqrt(5 + 2 * sqrt(5))



Edited: 4 Mar 2007, 12:03 p.m.


This still can be improved by someone who knows the HP-17BII/II+ solver better, like placing SIN, COS and TAN into a single menu group

I think this can be done, but it looks like it can get complicated when the equations themselves are "busy". Probably need to work it out on paper first, then enter it in.

I am curious if they work on the HP-17BII+.

I have entered only the SIN equation from set 1, and it works beautifully. Very fast. Solving for arcsine iteratively takes a couple of seconds and requires an intelligent initial guess lest one get a result outside of the -90 to +90 degree range that may not be trustworthy. Of note, naively solving for arcsin(1) from initial guesses of 85 degrees converges not to 90 degrees but rather 89.9998857789, which is expected since the sine of the latter is very close indeed to 1--0.999999999998 on my HP49G+.

This is a lot of typing and I am very interested in learning more about the Solver and combining these into one omnibus equation that reuses the repeated polynomial material with the L() and G() commands. It would be nice to have all of this stuff in one solver menu, but this means it all needs to be in one huge equation with conditionals built in. Complicated!


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