pi to 24 significant digits; TI sin(x) bug HP doesn't have
Rick Nungester
use of sin(x) ~= x for small x (in radians). I am using an HP-32SII,
which provides 12 significant digits:
Enter pi. See 3.14159265359.
3.14159265358 has to be slightly less than pi.
sin(3.14159265358) = 9.79323846264e-12
pi ~= 3.14159265358 9 79323846264 (24 digits)
Trying the same technique on a TI-83+SE (10 significant digits, so I
would hope of easily getting 20) shows a problem with sin(x):
Enter pi. See 3.141592654. So far so good.
3.141592653 has to be slightly less than pi.
sin(3.141592653) = 5.898e-10. PROBLEM. The answer has dropped to 4
significant digits instead of 10, so the TI misses 6 important
significant digits for arguments close to pi. The HP calculator
correctly gives:
sin(3.141592653) ~= 5.89793238463e-10, or
pi ~= 3.141592653 5 89793238463
I understand why the TI does this, and it isn't optimum.
Rick
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XYZ
...And that's why we don't use TI's! (even though they just may be
constructed better now days, HP calc software rocks :-)))
Bhuvanesh
TI calc software rocks too! :-)
Just chirping in for no reason,
Bhuvanesh.
Edward Sanford Sutton, III
Thanks for the cool idea. my ti83 was stolen, but my ti86 and ti89
can seem to check the results, but they like to round too much, which
makes the truth hard to see. =(
Something seems flakey somewhere in this to me though. if you need
sin(x)~=x to have a value very close to x, (taking note that
3.14159265358 is less than pi), is there a way to use 3.14159265359 to
find the extra pi digits since it is closer to pi (and also less than
pi), while not being equal to pi?
By the way, HP49G returned the same results as your HP-32SII.
Ed Sutton
Tom Lake
> can seem to check the results, but they like to round too much, which
> makes the truth hard to see. =(
> Something seems flakey somewhere in this to me though. if you need
> sin(x)~=x to have a value very close to x, (taking note that
> 3.14159265358 is less than pi), is there a way to use 3.14159265359 to
> find the extra pi digits since it is closer to pi (and also less than
> pi), while not being equal to pi?
The Pi key (2nd ^) gives the value of Pi to as many places as the calculator
can use anyway so what's point in computing it?
--
Tom Lake
Experience keeps a dear school but fools will learn in no other - Poor
Richard's Almanack
Arnaud Amiel
>
> Thanks for the cool idea. my ti83 was stolen, but my ti86 and ti89
> can seem to check the results, but they like to round too much, which
> makes the truth hard to see. =(
> Something seems flakey somewhere in this to me though. if you need
> sin(x)~=x to have a value very close to x, (taking note that
> 3.14159265358 is less than pi), is there a way to use 3.14159265359 to
> find the extra pi digits since it is closer to pi (and also less than
> pi), while not being equal to pi?
> By the way, HP49G returned the same results as your HP-32SII.
> Ed Sutton
Of course, it works but 3.14159265359 is very stlightly more than pi so you get
sin(3.14159265359)=-2.0676154E-13 Which is by how much it is slightly bigger.
1+(-.2067154)=.7932846
Which are the numbers you are after.
Arnaud
Edward Sanford Sutton, III
Hmm, seems I managed to screw up my decimal place when checking my
last digits quite a few times yesterday then while looking at it. That
did answer my next question of if it was still usable though too so
thank you very much. Now I wonder what other fun things there are to
do with my calc. =)
Ed Sutton