[HP 35s] Hosoda trig program giving incorrect answers to certain angles

08052015, 02:36 PM
(This post was last modified: 08052015 04:30 PM by Marcio.)
Post: #1




[HP 35s] Hosoda trig program giving incorrect answers to certain angles
Hello all,
After clearing all variables and registers, I noticed that Hosoda gives wrong answers to certain angles (cosine) on my 35s: \[ \begin{matrix} & Hosoda & 35s & 34s & 50g \\ 5\frac { \pi }{ 180 } & 9.96194698092E1 & 9.96194698092E1 & 9.96194698092E1 & 9.96194698092E1 \\ 75\frac { \pi }{ 180 } & 2.58819045098E1 & 2.58819045098E1 & 2.58819045103E1 & 2.58819045108E1 \\ 89.999\frac { \pi }{ 180 } & 1.74532948958E5 & 1.74532948891E5 & 1.74532925187E5 & 1.74532948957E5 \\ 89.9999\frac { \pi }{ 180 } & 1.74532489662E6 & 1.74532489000E6 & 1.74532925262E6 & 1.74532489662E6 \end{matrix} \] Does anybody have any idea as to what is happening? Maybe I am missing something here? I have already doublechecked 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. 

08052015, 02:49 PM
Post: #2




RE: [HP 35s] Hosoda trig program giving incorrect answers for certain angles
(08052015 02:36 PM)Marcio Wrote: Hello all, Could it be related to the fact that near 90° the 35s trig functions have very limited accuracy? (about four digits only) Tom L Tom L Cui bono? 

08052015, 02:57 PM
(This post was last modified: 08052015 03:26 PM by Marcio.)
Post: #3




RE: [HP 35s] Hosoda trig program giving incorrect answers for certain angles
(08052015 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 (1E7°) 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. 

08052015, 03:17 PM
(This post was last modified: 08052015 03:29 PM by Gerald H.)
Post: #4




RE: [HP 35s] Hosoda trig program giving incorrect answers for certain angles
Hosoda's programmes only work in radian measures.
For 75°, ie 75 * pi / 180, the programme returned 2.58819045108E1 ie I did the >RAD by hand, not using the builtin function. Other values as you have them. 

08052015, 03:19 PM
(This post was last modified: 08052015 03:23 PM by Marcio.)
Post: #5




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
(08052015 03:17 PM)Gerald H Wrote: Hosoda's programmes only work in radian measures. Yes, I converted them to RAD before calling the routines. EDIT: The last digit of your answer reads 8. Is it not 3? 

08052015, 03:25 PM
(This post was last modified: 08052015 03:26 PM by Gerald H.)
Post: #6




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
I've now edited my posting to show I did not use the builtin >RAD function.


08052015, 03:29 PM
Post: #7




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles  
08052015, 03:31 PM
(This post was last modified: 08052015 03:32 PM by Gerald H.)
Post: #8




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
I, as a lazy user, think the conversion >RAD produces inaccuracies & Hosoda's programmes may be inaccurate near the cusp.


08052015, 03:44 PM
Post: #9




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
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. 

08052015, 03:47 PM
(This post was last modified: 08052015 03:50 PM by Marcio.)
Post: #10




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
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 

08052015, 03:50 PM
Post: #11




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
Try inputting 1.57079458147 on the 34S & see the value returned.


08052015, 04:21 PM
Post: #12




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
& on my trusty HP 48S
89.9999° COS returns 1.74532925199E6 & converted to radians 1.57079458147 returns1.74532489662E6 

08052015, 04:23 PM
(This post was last modified: 08052015 04:33 PM by Marcio.)
Post: #13




RE: [HP 35s] Hosoda trig program giving incorrect answers to certain angles
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 

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