Subject:
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Re: basic trigonometric functions on the handyboard..
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Newsgroups:
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lugnet.robotics.handyboard
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Date:
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Tue, 9 Mar 1999 21:40:15 GMT
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Original-From:
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Scott Harris <SRHARRIS@PRINCETON.nospamEDU>
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Viewed:
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3407 times
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A Taylor series isn't the way to go: they converge far too slowly.
Here is a polynomial fit to arccos(x):
arccos(x) ~ = 1.5708 - 1.0927 x + 4.358 x^3 - 0.8340 x^5
It differs from the exact value of arccos(x) by no more that 0.08 radians (4.6
degrees) in the range [-1,1].
If you need more accuracy, just fit a polynomial with more terms to arccos.
-Scott
Thomas Heidel wrote:
> Hi,
>
> The taylor for cos^-1 goes:
>
> cos^-1(x) = Pi/2- (x + 1/2*x^3/3 + 1/2*3/4*x^5/5 + 1/2*3/4*5/6*x^7/7
> ...)
>
> (which in fact is simply Pi/2 - sin^-1)
>
> The results are very good for small x. For x close to 1 you need many
> many
> elements of that series to be somehow accurate.
>
> "SHETTI.NITIN.MANGESH" wrote:
> >
> > Dear Berg,
> > You can perhaps express cos^-1 in the forms of a Taylor series and
> > use that series for finding the approximate value. I have however not
> > tried it.
> > There is no math function for inverse cosine.Refer to handy board
> > manual available el.www.mit.media.edu for details on IC.
> > Yours sincerely,
> > Nitin
> >
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