Could someone do a calculation on a real 71B?
01-15-2017, 08:59 AM
Post: #1
 zeno333 Member Posts: 189 Joined: Mar 2015
Could someone do a calculation on a real 71B?
Could someone get the real HP 71Bs answer to the SIN of exactly 3.141592654 radians??? I am looking for from a actual unit and not an emulator.
01-15-2017, 09:24 AM
Post: #2
 Gerson W. Barbosa Senior Member Posts: 1,333 Joined: Dec 2013
RE: Could someone do a calculation on a real 71B?
-4.10206761537E-10

Gerson.
01-15-2017, 09:26 AM
Post: #3
 Didier Lachieze Senior Member Posts: 1,221 Joined: Dec 2013
RE: Could someone do a calculation on a real 71B?
My 71b returns: -4.10206761537E-10, same value as my 48SX , 48GX and HP Prime.

I get the same result also on the go71b emulator.
01-16-2017, 10:31 AM (This post was last modified: 01-16-2017 10:34 AM by EdS2.)
Post: #4
 EdS2 Member Posts: 234 Joined: Apr 2014
RE: Could someone do a calculation on a real 71B?
It's more enlightening to ask for the sin of a number just below pi, because then you get more digits of pi.

So, sin(3.14159265) for example, should give you
3.58979323846E-9
and
sin(3.141592653) should give
5.89793238463E-10

These are very accurate results! (I used Olivier de Smet's go48g emulator on Android, that's the one closest to hand. Oh, but the HP35s gives the same.)
01-16-2017, 11:14 AM (This post was last modified: 01-16-2017 11:17 AM by Thomas Okken.)
Post: #5
 Thomas Okken Senior Member Posts: 1,055 Joined: Feb 2014
RE: Could someone do a calculation on a real 71B?
(01-16-2017 10:31 AM)EdS2 Wrote:  It's more enlightening to ask for the sin of a number just below pi, because then you get more digits of pi.

Neat! I never realized that.
It works for the number just above pi, too; you just get the ten's complement of those extra digits:

Code:
10.00000000000E-10 -4.10206761537E-10 ------------------  5.89793238463E-10

I guess the point is that the calculator performs argument reduction using an extended-precision approximation of pi. Next question, for extra credit: how many digits?
01-16-2017, 01:18 PM
Post: #6
 J-F Garnier Senior Member Posts: 450 Joined: Dec 2013
RE: Could someone do a calculation on a real 71B?
(01-16-2017 11:14 AM)Thomas Okken Wrote:  I guess the point is that the calculator performs argument reduction using an extended-precision approximation of pi. Next question, for extra credit: how many digits?

See this discussion.

J-F
01-16-2017, 01:40 PM
Post: #7
 Gerson W. Barbosa Senior Member Posts: 1,333 Joined: Dec 2013
RE: Could someone do a calculation on a real 71B?
(01-16-2017 11:14 AM)Thomas Okken Wrote:
(01-16-2017 10:31 AM)EdS2 Wrote:  It's more enlightening to ask for the sin of a number just below pi, because then you get more digits of pi.

Neat! I never realized that.
It works for the number just above pi, too; you just get the ten's complement of those extra digits:

Code:
10.00000000000E-10 -4.10206761537E-10 ------------------  5.89793238463E-10

I guess the point is that the calculator performs argument reduction using an extended-precision approximation of pi. Next question, for extra credit: how many digits?

That's an old trick (see http://www.hpmuseum.org/forum/post-18529.html#pid18529), but I wasn't aware of the 10's complement part. Thanks!

Gerson.
01-17-2017, 12:02 AM
Post: #8
 KeithB Member Posts: 240 Joined: Jan 2017
RE: Could someone do a calculation on a real 71B?
You did not ask, but sin(PI) is:
-2.06761537357e-13
01-17-2017, 03:19 AM
Post: #9
 Thomas Okken Senior Member Posts: 1,055 Joined: Feb 2014
RE: Could someone do a calculation on a real 71B?
(01-16-2017 01:18 PM)J-F Garnier Wrote:
(01-16-2017 11:14 AM)Thomas Okken Wrote:  I guess the point is that the calculator performs argument reduction using an extended-precision approximation of pi. Next question, for extra credit: how many digits?

See this discussion.

J-F

Ah, yes. Thank you!

That link led me even further back, to this discussion, where Hugh Steers points out that you need lots of digits of pi if you want to calculate the sine, in radians, for very large arguments. He explained this to me once when we were discussing his BCD20 floating-point library, which I had noticed contained pi to several hundred digits.
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