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[HP 35s] Hosoda trig program giving incorrect answers to certain angles - Marcio - 08-05-2015 02:36 PM
Hello all,
After clearing all variables and registers, I noticed that Hosoda gives wrong answers to certain angles (cosine) on my 35s:
\[
\begin{matrix} & Hosoda & 35s & 34s & 50g \\ 5\frac { \pi }{ 180 } & 9.96194698092E-1 & 9.96194698092E-1 & 9.96194698092E-1 & 9.96194698092E-1 \\ 75\frac { \pi }{ 180 } & 2.58819045098E-1 & 2.58819045098E-1 & 2.58819045103E-1 & 2.58819045108E-1 \\ 89.999\frac { \pi }{ 180 } & 1.74532948958E-5 & 1.74532948891E-5 & 1.74532925187E-5 & 1.74532948957E-5 \\ 89.9999\frac { \pi }{ 180 } & 1.74532489662E-6 & 1.74532489000E-6 & 1.74532925262E-6 & 1.74532489662E-6 \end{matrix} \]
Does anybody have any idea as to what is happening? Maybe I am missing something here?
I have already double-checked all program lines and everything is exactly as before.
Very much appreciated.
Marcio
CORRECTION: Hosoda trig program is working as expected, it was I who "forgot" about the significant loss of accuracy that occurs while converting from DEG to RAD, as pointed out by our dear friend Gerald.
RE: [HP 35s] Hosoda trig program giving incorrect answers for certain angles - toml_12953 - 08-05-2015 02:49 PM
(08-05-2015 02:36 PM)Marcio Wrote: Hello all,
After clearing all variables and registers, I noticed that Hosoda gives wrong answers to certain angles (cosine) on my 35s:
\[
\begin{matrix} & Hosoda & 35s & 34s \\ 5 & 9.96194698092E-1 & 9.96194698092E-1 & 9.96194698092E-1 \\ 75 & 2.58819045098E-1 & 2.58819045103E-1 & 2.58819045103E-1 \\ 89.999 & 1.74532948958E-5 & 1.74532925091E-5 & 1.74532925191E-5 \\ 89.9999 & 1.74532489662E-6 & 1.74532925000E-6 & 1.74532925199E-6 \end{matrix}\]
Does anybody have any idea as to what is happening? Maybe I am missing something here?
I have already double-checked all program lines and everything is exactly as before.
Very much appreciated.
Marcio
Could it be related to the fact that near 90° the 35s trig functions have very limited accuracy? (about four digits only)
Tom L
RE: [HP 35s] Hosoda trig program giving incorrect answers for certain angles - Marcio - 08-05-2015 02:57 PM
(08-05-2015 02:49 PM)toml_12953 Wrote: Could it be related to the fact that near 90° the 35s trig functions have very limited accuracy? (about four digits only)Well, the 35s does have troubles getting all digits correct when the angles are very small (1E-7°) or near 90°, as in 89.9999° (four decimals, not three), but the Hosoda code, a 3rd party program, is supposed to get digits right. I myself have been working with it a lot lately and yesterday, after clearing everything, I noticed this weird behaviour. I suspect it has to do with some registers not being real numbers, and they got erased, I know, it seems crazy but it is all I can remember from yesterday. To make matters worse, while \(e^x\) is stable across the entire domain on the 35s, \(e^{ix}\) shows the same instability as observed on the trig functions calculated by the 35s on those very same angles.
Tom L
RE: [HP 35s] Hosoda trig program giving incorrect answers for certain angles - Gerald H - 08-05-2015 03:17 PM
Hosoda's programmes only work in radian measures.
For 75°, ie 75 * pi / 180, the programme returned
2.58819045108E-1
ie I did the ->RAD by hand, not using the built-in function.
Other values as you have them.
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Marcio - 08-05-2015 03:19 PM
(08-05-2015 03:17 PM)Gerald H Wrote: Hosoda's programmes only work in radian measures.
For 75°, ie 75 * pi / 180, the programme returned
2.58819045108E-1
Other values as you have them.
Yes, I converted them to RAD before calling the routines.
EDIT: The last digit of your answer reads 8. Is it not 3?
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Gerald H - 08-05-2015 03:25 PM
I've now edited my posting to show I did not use the built-in ->RAD function.
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Marcio - 08-05-2015 03:29 PM
(08-05-2015 03:25 PM)Gerald H Wrote: I've now edited my posting to show I did not use the built-in ->RAD function.
That's alright.
Regarding the incorrect answers, what do you, as an experienced user, think?
Thanks
Marcio
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Gerald H - 08-05-2015 03:31 PM
I, as a lazy user, think the conversion ->RAD produces inaccuracies & Hosoda's programmes may be inaccurate near the cusp.
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Gerald H - 08-05-2015 03:44 PM
89.9999 ->RAD gives 1.57079458147 on the 35S
actual value is more like 1.57079458146564...
so you can't expect so much accuracy from the result.
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Marcio - 08-05-2015 03:47 PM
My dear Gerald, with all due respect, I think you're missing the point. Please, have another look at the table at the beginning. Until recently, the Hososa code I have here gave the same answers as the 34s, which uses more digits deep inside.
Thanks
Marcio
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Gerald H - 08-05-2015 03:50 PM
Try inputting 1.57079458147 on the 34S & see the value returned.
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Gerald H - 08-05-2015 04:21 PM
& on my trusty HP 48S
89.9999° COS returns 1.74532925199E-6
& converted to radians
1.57079458147 returns1.74532489662E-6
RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles - Marcio - 08-05-2015 04:23 PM
Yes, you're 100% correct. It was just another lapse of mine! I never thought the impact would be that big though! Thank you for pointing that out.
EDIT: I have also updated the table.
Marcio