Can someone do a calculation on a TI Inspire CAS?

01292019, 01:21 AM
Post: #1




Can someone do a calculation on a TI Inspire CAS?
I do not have access to a TI Inspire CAS, and was wondering if someone can tell me the result for the SIN of exactly 3.141592654 radians on it. Thanks


01292019, 02:41 AM
(This post was last modified: 01292019 03:30 AM by zeno333.)
Post: #2




RE: Can someone do a calculation on a TI Inspire CAS?
PS, I know what the correct answer is to as many digits as I care to get, (via Mathematica), but curious how accurate the TI is compared to some HPs that get it correct to 12 significant digits ...TIs in the past have not been as accurate as certain HPs for Trig functions...


01292019, 03:11 AM
Post: #3




RE: Can someone do a calculation on a TI Inspire CAS?
My TInspire cx CAS, given the following in RAD mode:
sin(3.141592654) gives: 4.102e10 

01292019, 06:07 AM
Post: #4




RE: Can someone do a calculation on a TI Inspire CAS?
That's pretty accurate.
For values of x around \(\pi\), \(sin(x) \approx \pix\) The value of \(\pi\) is closer to 3.14159265358979, and \(3.141592653589793.141592654=4.1021\times10^{10}\) so I'd say this machine is right on the money. The inaccuracy here isn't in the calculator, it's in the assumed value of \(\pi\). 

01292019, 06:37 AM
Post: #5




RE: Can someone do a calculation on a TI Inspire CAS?
Hallo Zeno33,
on a TI nspire CX (not the CAS model) I got sin(3.141592654)=4.102E10 I hope that helps, Thomas 

01292019, 07:58 AM
Post: #6




RE: Can someone do a calculation on a TI Inspire CAS?
Hmm  you're only getting four digits of result. Normally we'd say that's not very accurate.
For this kind of calculation the calculator does need to do more work than usual  it helps to have an internal value for pi which is twice the number of digits displayed  but from a user perspective, how it does it isn't the same question as how accurate it is. Because the input value is close to pi, there's a possibility of loss of precision, which is what we see here. To be fair to TI, most calculators don't do much better and may even do worse. 

01292019, 08:23 AM
Post: #7




RE: Can someone do a calculation on a TI Inspire CAS?  
01292019, 11:56 AM
(This post was last modified: 01302019 10:14 AM by pier4r.)
Post: #8




RE: Can someone do a calculation on a TI Inspire CAS?
(01292019 02:41 AM)zeno333 Wrote: PS, I know what the correct answer is to as many digits as I care to get, (via Mathematica), but curious how accurate the TI is compared to some HPs that get it correct to 12 significant digits ...TIs in the past have not been as accurate as certain HPs for Trig functions... Curious, what answer do you expect? Precisely 0? In that case the sin function would have edge cases hardcoded is the most likely case. Wikis are great, Contribute :) 

01292019, 04:21 PM
Post: #9




RE: Can someone do a calculation on a TI Inspire CAS?
FWIW, my TI30X Pro MathPrint displays the answer 4.102067615e10, with an internal result of 4.102067615374. That seems to be pretty accurate. (For comparison, HP42S shows 4.10206761537e10, and DM42/Free42 shows 4.102067615373566167089928953969909e10.)
— Ian Abbott 

01292019, 04:53 PM
Post: #10




RE: Can someone do a calculation on a TI Inspire CAS?
(01292019 11:56 AM)pier4r Wrote:(01292019 02:41 AM)zeno333 Wrote: PS, I know what the correct answer is to as many digits as I care to get, (via Mathematica), but curious how accurate the TI is compared to some HPs that get it correct to 12 significant digits ...TIs in the past have not been as accurate as certain HPs for Trig functions... Yeah, I'd rather get the real answer rather than have the calculator try to fudge by showing 0. Tom L Cui bono? 

01292019, 05:09 PM
(This post was last modified: 01292019 05:27 PM by Albert Chan.)
Post: #11




RE: Can someone do a calculation on a TI Inspire CAS?
(01292019 07:58 AM)EdS2 Wrote: ... it helps to have an internal value for pi which is twice the number of digits We need even more digits of pi to handle bigger argument. Example, assumed all calculation in 24 digits precision : sin(411557987) = sin(411557987 mod (2 * pi)) ~ sin(411557987 mod (2 * 3.14159265358979323846264)) = sin(2.53671649518336E9) = 2.5367164951833599972794E9 Rounded back to 12 digits, sin(X) = 2.53671649518E9. 24 digits math only get 7 accurate digits ! Using spigot calculator: > spigot printf=%.12g sin(411557987) 2.53671605196e09 see FSIN "bug": Intel underestimates error bounds by 1.3 quintillion 

01292019, 09:01 PM
Post: #12




RE: Can someone do a calculation on a TI Inspire CAS?
AFAICT, 4.102e10 is the most precise answer for sin(3.141592654) on the TI Nspire CX CAS running OS 4.5.0.1180. I've been through various display settings and have been unable to extract any more digits of precision.
— Ian Abbott 

01302019, 02:32 AM
Post: #13




RE: Can someone do a calculation on a TI Inspire CAS?
(01292019 06:07 AM)grsbanks Wrote: That's pretty accurate. I was not assuming anything...I was asking for the SIN of a specific input, and the HPs give a much higher accuracy than the TIZs...The HP 28, 42S, 48 series 50G and prime etc give the answer correct to 12 digits, the TI is not even close. 

01302019, 02:34 AM
Post: #14




RE: Can someone do a calculation on a TI Inspire CAS?
(01292019 11:56 AM)pier4r Wrote:(01292019 02:41 AM)zeno333 Wrote: PS, I know what the correct answer is to as many digits as I care to get, (via Mathematica), but curious how accurate the TI is compared to some HPs that get it correct to 12 significant digits ...TIs in the past have not been as accurate as certain HPs for Trig functions... The correct answer to 12 digits is 4.10206761537 E10...This problem is described in detail in the optional HP 15C Advanced Functions Handbook... 

01302019, 09:07 AM
Post: #15




RE: Can someone do a calculation on a TI Inspire CAS?
(01302019 02:32 AM)zeno333 Wrote: I was not assuming anything...I was asking for the SIN of a specific input, and the HPs give a much higher accuracy than the TIZs...The HP 28, 42S, 48 series 50G and prime etc give the answer correct to 12 digits, the TI is not even close. I'd say that depends on the particular model. The HP41 series, the 67, 15C and – I suppose – other 10digit devices return 4,10 E–10. Which is what you get with a pi constant rounded to the internal 13 digits of these calculators. Dieter 

01302019, 09:18 AM
(This post was last modified: 01302019 09:20 AM by EdS2.)
Post: #16




RE: Can someone do a calculation on a TI Inspire CAS?
For those still unsure, the key here is that 3.1415926534 is not pi, it is an approximation to pi. So, an exact calculation of sin(x) using this number should not be zero  it should be approximately zero. (Edit: whereas sin(180) in degree mode should be exactly zero.)
Interestingly enough, HP themselves said the same thing, in 1976: Quote:There is a point where the new algorithms appear at first glance to be less accurate. If we calculate tan π in radians, the answer is 4.10 E 10 on the HP91 whereas the HP55 yields 0. This is misleading, for π on the keyboard should really be labeled π₁₀, showing that it is ten digits of π. ThusSee The New Accuracy: Making 2³ = 8, by Dennis. W. Harms in HP Journal, November 1976 page 17. 

02092019, 11:38 PM
Post: #17




RE: Can someone do a calculation on a TI Inspire CAS?
Hello!
If you are using the sin(pi) on a TInspire you get zero. But I think, the value of 3.1415926534 for pi is not a good choice. For calculation in real world physics normally you don't need so many significant digits, so I think using pi directly is ok. And I have tried several calcs: DM42: 1.897932384626433832783634455164435e10 DM15: 5.9e10 fx991DE PLUS: 1.898e10 HP300s+: 1.898e10 numworks: 1.8997932e10 HP35s: 1.89793238e10 2DS: 0 I have input the number from the last post 3.1415926534 (and not 3.141592654) with all digit if possible. As you can see one digit more, you get a result half as big as the other (4.102069e10 by numworks). So I think rounding to 0 is fine for real world problems. That's the reason HP choice FIX 4 as default for many calcs. Bernd 

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