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Subject: 
Re: basic trigonometric functions on the handyboard..
Newsgroups: 
lugnet.robotics.handyboard
Date: 
Tue, 9 Mar 1999 20:33:22 GMT
Original-From: 
Thomas Heidel <{theidel@advis.}SayNoToSpam{de}>
Viewed: 
913 times
  
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

On Tue, 9 Mar 1999, Guy & Gad Berg wrote:

Hi.
We've been trying to build an algorithm which will allow our HB to
travel between given points.
We need to use the inverse cosine function (cos^-1), how can we do that?
Is there a math library which contains this and other trig functions?

Thanks,
Guy.





Message has 1 Reply:
  Re: basic trigonometric functions on the handyboard..
 
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 (...) (25 years ago, 9-Mar-99, to lugnet.robotics.handyboard)

Message is in Reply To:
  Re: basic trigonometric functions on the handyboard..
 
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 (...) (25 years ago, 9-Mar-99, to lugnet.robotics.handyboard)

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