tan(pi/24), what is the correct result?

09052016, 04:15 PM
(This post was last modified: 09052016 07:10 PM by Dol.)
Post: #1




tan(pi/24), what is the correct result?
tan(pi/24), what is the correct result?
EDIT: ( Correct result should be close to .131652) Google: 0.131652498 Torsten Manz HP15c Emulator on Windows: 0,1316524976 Greg Hewill HP15c Simulator: 0.0022846346233134987 Windows Calculator: 0,00228463462331349894308299181234 EDIT: FREE42 Windows/iOS: 0.0023 What does: HP41C HP42 HP48SX Orig HP15C HP15LE HP11C HP Prime HP35S bc Give as a result? /Check results in posts below/ 

09052016, 04:27 PM
Post: #2




RE: tan(pi/24), what is the correct result?
Deg/Rad/Grad?


09052016, 04:55 PM
Post: #3




RE: tan(pi/24), what is the correct result?  
09052016, 05:34 PM
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RE: tan(pi/24), what is the correct result?  
09052016, 05:56 PM
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RE: tan(pi/24), what is the correct result?  
09052016, 06:33 PM
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RE: tan(pi/24), what is the correct result?  
09052016, 06:48 PM
Post: #7




RE: tan(pi/24), what is the correct result?  
09052016, 06:58 PM
(This post was last modified: 09052016 07:45 PM by DavidM.)
Post: #8




RE: tan(pi/24), what is the correct result?
(09052016 04:15 PM)Dol Wrote: tan(pi/24), what is the correct result? How do you define "correct" for an approximate number in decimal form using approximate intermediate results of varying precision? That said, here's a few more results for TAN(pi/24). RAD mode WolframAlpha using "N[Tan[Pi/24], 80]" as input (for reference): 0.13165249758739585347152645740971710359281410222323757355356532578975983901062203 HP 48sx Standard Precision: 0.131652497588 HP 48sx Extended Precision (using SysRPL, pi = 3.14159265358979): 0.131652497587394 HP 50g Approximate Mode (Standard Precision): 0.131652497588 HP 50g Extended Precision (using SysRPL): 0.131652497587394 HP 50g Using LongFloat Library set to 80 digits: 0.13165249758739585347152645740971710359281410222323757355356532578975983901062203 (EDIT: added results for degrees) DEG mode WolframAlpha using "N[Tan[Pi/24], 80]" as input (for reference): 0.0022846346233134989430829918123351051243508494673687155701324734301154772268981872 HP 48sx Standard Precision: 0.00228463462332 HP 48sx Extended Precision (using SysRPL, pi = 3.14159265358979): 0.00228463462331348 HP 50g Approximate Mode (Standard Precision): 0.00228463462332 HP 50g Extended Precision (using SysRPL): 0.00228463462331348 HP 50g Using LongFloat Library set to 80 digits: 0.0022846346233134989430829918123351051243508494673687155701324734301154772268981872 

09052016, 07:05 PM
(This post was last modified: 09052016 07:19 PM by Dol.)
Post: #9




RE: tan(pi/24), what is the correct result?
(09052016 06:33 PM)JF Garnier Wrote:(09052016 04:15 PM)Dol Wrote: tan(pi/24), what is the correct result?RPN: 3 SQRT 2 SQRT  LASTX 1  * Thanks! How come Windows 7 calculator gets its so wrong? Also I tried free42 on iOS and it also gets 0.0023 (wrong). Ill update the initial post with the new values. EDIT: It seems everyone gets the same values when in RAD mode, free42, Win Calculator, etc however in DEG mode maybe some emulators do RAD implicitly? I am confused! 

09052016, 07:46 PM
(This post was last modified: 09052016 07:52 PM by Dieter.)
Post: #10




RE: tan(pi/24), what is the correct result?
(09052016 07:05 PM)Dol Wrote: How come Windows 7 calculator gets its so wrong? There is nothing wrong here. The tangent of pi/24 degrees is 0,00228463462331349894308299181233... The tangent of pi/24 radians is 0,131652497587395853471526457409... The calculators you used were once set to degrees and once to radians. That's it. And if you set Free42 to ALL display mode instead of FIX 4 you will see the fullprecision result instead of just 0,0023. Or simply press the SHOW key. So just set the correct angular mode and you'll get a correct result. With all of the mentioned calculators. There's nothing wrong with them at all. Within working precision, that is. A 10digit calculator will not evaluate the tangent of pi/24, but of {3,141592654/24 rounded to 10 digits}, i.e. it will calculate tan(0,1308996939) = 0,00284634623 (degrees) resp. 0,1316524976 (radians). Dieter 

09052016, 07:52 PM
(This post was last modified: 09052016 08:17 PM by Vtile.)
Post: #11




RE: tan(pi/24), what is the correct result?
*meh*
Foolery number, it is pretty much same which ever way you handle it. Is that correct answer. 

09062016, 01:42 AM
Post: #12




RE: tan(pi/24), what is the correct result?
HP15C deg=0.002284634623 (observing all digits f+PREFIX)
Rad=0.1316524976 observing all digits f+PREFIX) 

09062016, 03:34 AM
Post: #13




RE: tan(pi/24), what is the correct result?
(09052016 07:46 PM)Dieter Wrote:(09052016 07:05 PM)Dol Wrote: How come Windows 7 calculator gets its so wrong? OK, I understand about the precision, no issues. As of now, the problem remains that Torsten Manz HP15c calculator gives the RAD result even in DEG mode. Can someone else confirm this behavior so we can send a bug report to Torsten? That is why I got confused and started trying different calculators in DEG mode. Google displays the result in RAD (without explicit mentioning about RAD/DEG) Regards Fredrik 

09062016, 03:58 AM
Post: #14




RE: tan(pi/24), what is the correct result?
WP34S TAN(pi/24) DEG
WP34S TAN(pi/24) RAD
Firmware: 34S 3.3[Print]3844 

09062016, 04:06 AM
(This post was last modified: 09062016 04:25 AM by Nick.)
Post: #15




RE: tan(pi/24), what is the correct result?
(09062016 03:34 AM)Dol Wrote: As of now, the problem remains that Torsten Manz HP15c calculator gives the RAD result even in DEG mode. Can someone else confirm this behavior so we can send a bug report to Torsten? The following behavior may apply: From the HP15C Owner's Handbook (2011) p.121 Quote:Note: In Complex mode (signified by the C annunciator), the HP15C performs all trigonometric functions using radians. The trigonometric mode annunciator in the display (RAD, GRAD, or blank for Degrees) applies to two functions only: [>R] and [>P] (as explained later in this section). Quote:To deactivate Complex mode, clear flag 8 (keystroke sequence: [g] [CF] 8). The C annunciator will disappear. HP15C Owner's Handbook (2011) [hp.com] HP15C Advanced Functions Handbook (1982) [hp.com] Edit: Added HP15C Manuals Links 

09062016, 05:01 AM
Post: #16




RE: tan(pi/24), what is the correct result?
(09062016 04:06 AM)Nick Wrote:(09062016 03:34 AM)Dol Wrote: As of now, the problem remains that Torsten Manz HP15c calculator gives the RAD result even in DEG mode. Can someone else confirm this behavior so we can send a bug report to Torsten? That was it, case closed!! 

09062016, 06:29 AM
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RE: tan(pi/24), what is the correct result?  
09062016, 08:19 AM
Post: #18




RE: tan(pi/24), what is the correct result?
(09052016 04:15 PM)Dol Wrote: tan(pi/24), what is the correct result? The correct result is close to 0.131652. When you say tan(x), x is an angle in radians, unless you specifically say otherwise, like saying tan(x°). I admit I didn't read your original post carefully enough. I thought you were looking to compare the numerical accuracy of various calculators; I didn't realize you were unaware of the degrees vs. radians thing. :D 

09062016, 02:01 PM
Post: #19




RE: tan(pi/24), what is the correct result?
HP 10s+
0,131652497 HP 300s+ 0,1316524976 HP 35s 1,31652497588e1 HP 40gs CAS 0,131652497588 HOME 0,131652497588 

09062016, 03:18 PM
(This post was last modified: 09062016 03:21 PM by toml_12953.)
Post: #20




RE: tan(pi/24), what is the correct result?
(09052016 04:15 PM)Dol Wrote: tan(pi/24), what is the correct result? When in Radian mode, Windows calculator (Windows 10 version) gives 0.13165249758739585347152645740972 You were in Degree mode when you did your calculation. Tom L Tom L Cui bono? 

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