Re: How does the calculator calculate cos(x)?
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Re: How does the calculator calculate cos(x)?
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To: CALC-TI@LISTS.PPP.TI.COM
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Subject: Re: How does the calculator calculate cos(x)?
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From: "~padgett"@MCMASTER.CA
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Date: Thu, 23 Oct 1997 22:47:35 GMT
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Organization: McMaster University, Hamilton, Ontario, Canada (NewServer)
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References: <19971018135201.JAA10220@ladder02.news.aol.com>
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Reply-To: "~padgett"@MCMASTER.CA
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Xref: paladin.american.edu bit.listserv.calc-ti:18085
On 18 Oct 1997 13:52:55 GMT, archdluxxx@aol.com (ArchDluxxx) wrote:
>I would like to learn how the TI's actually calculate cos(x). Can anybody help
> me!!!
Many times polynomial function are used. See the following article for
information.
Neil Padgett
--- BEGIN ARTICLE ---
Originally posted by Francois Charton <deef@pobox.oleane.com> to
comp.graphics.algorithms with
subject: Re: Sine (or Cosine) Algo. needed
on Fri, 27 Dec 1996 16:10:02 +0100
[clip]
*Important* all this calculation is done in radians : 180 degrees is
PI
(3.141592...) radians, 90 degrees is PI/2... if you plan to use many
trig
functions in your life, you'd better get used to them : they are a
must!
To convert your angle from degrees to radians divide it by 180 ad
multiply is by PI
angle_in_radians=angle_in_degrees * PI /180
now the formulae :
cos(x) = 1 - 0.49999 99963 x^2 + 0.04166 66418 x^4 - 0.00138 88397 x^6
+ 0.00002 47609 x^8 - 0.00000 02605 x^2
and
sin(x) = x - 0.16666 66664 x^3 + 0.00833 33315 x^5 - 0.00019 84090 x^7
+ 0.00000 27526 x^9 - 0.00000 00239 x^11
These two functions approximate sin() and cos() with over 8 decimal
places accuracy, and should be enough precise nearly everytime (they
are
actually those used by pocket calculators). [I took them in Handbook
of
Mathematical Functions, by Abramowitz and Stegun]
[clip some more]
--- END ARTICLE ---
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