01-15-2017, 08:59 AM

01-15-2017, 09:24 AM

-4.10206761537E-10

Gerson.

Gerson.

01-15-2017, 09:26 AM

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.

I get the same result also on the go71b emulator.

01-16-2017, 10:31 AM

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.)

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

(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

(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

(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

You did not ask, but sin(PI) is:

-2.06761537357e-13

-2.06761537357e-13

01-17-2017, 03:19 AM

(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.