Subject:
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Re: Inversine sine function
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Newsgroups:
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lugnet.robotics.handyboard
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Date:
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Mon, 13 Dec 1999 06:16:02 GMT
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Viewed:
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3850 times
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This polynomial approximation looks better:
ArcSin(x) = Pi/2 - Sqrt(1-x)*(a(0) + a(1)*x + a(2)*x^2 + a(3)*x^3
+ a(4)*x^4 + a(5)*x^5 + a(6)*x^6 + a(7)*x^7 )
where
a(0) = 1.57079 63050
a(1) = -0.21459 88016
a(2) = 0.08897 89874
a(3) = -0.05017 43046
a(4) = 0.03089 18810
a(5) = -0.01708 81256
a(6) = 0.00667 00901
a(7) = -0.00126 24911
Reference: Abramowitz and Stegun, Handbook of Mathematical Functions,
Dover, 9th printing, 1972. p 81.
Caveat: I haven't used this one either, but the authors claim better
than 2e-8 accuracy for 0<=x<=1, which is much better than the series
in my first reply.
Again, good luck.
John C.
In lugnet.robotics.handyboard, John Cromer writes:
> In lugnet.robotics.handyboard, Jean-Michel Mongeau writes:
> > Hello,
> > I would like to calculate an inverse sine (arcsin) function for one of
> > my
> > application. Does anyone know the algorithm of this trigonometric function?
> >
> > Thank you,
> > J.M. Mongeau
>
> You might give this a try (for -1 < x < 1):
>
> ArcSin(x) = x + a(1)*x^3 + a(2)*x^5 + a(3)*x^7 + ... etc.
>
> with
> a(1) = 0.1666666667
> a(2) = 0.0750000000
> a(3) = 0.0446428571
> a(4) = 0.0303819444
> a(5) = 0.0223721599
> a(6) = 0.0173527644
> a(7) = 0.0139648437
> a(8) = 8.0115518009 (?)
This should be 0.0115518009, but really, don't bother....
> a(9) = 0.0097616095
> a(10)= 0.0083903358
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Message is in Reply To:
 | | Re: Inversine sine function
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| (...) You might give this a try (for -1 < x < 1): ArcSin(x) = x + a(1)*x^3 + a(2)*x^5 + a(3)*x^7 + ... etc. with a(1) = 0.1666666667 a(2) = 0.0750000000 a(3) = 0.0446428571 a(4) = 0.0303819444 a(5) = 0.0223721599 a(6) = 0.0173527644 a(7) = (...) (27 years ago, 13-Dec-99, to lugnet.robotics.handyboard)
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