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Message-ID: <200401281455.17651.royward@physics.otago.ac.nz>
Date: Wed, 28 Jan 2004 14:55:17 +1300
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From: Roy Ward <royward@PHYSICS.OTAGO.AC.NZ>
Subject: Re: [OT:] Curves intersection
Comments: To: Carlos Marcano <carlosmarcano78@cantv.net>
To: PICLIST@MITVMA.MIT.EDU
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On Wednesday 28 January 2004 14:34, Carlos Marcano wrote:
> Hi all:
>
> I got to admit that I am struggling with something that I should know =
as
> an engineer. I need to find analitically the points of intersection of two
> curves, that is:
>
> I) y=3D 1-(x*x)
>
> II) y=3D sen(x)
I assume that you mean y=3Dsin(x)
> Normally that would be as simple as doing I=3DII and resolving but in this
> case the fact that II is a trigonometrical ecuation brings some issues to
> the resolution. Having 1 - (x*x) =3D sen(x) I can=B4t find a way to get =
the
> posible values for x. I could try a graphical solution but I want the
> analitical (i.e. numerical) solution. Any ideas?
I'm pretty sure there isn't an analytical (btw, analytical !=3D numerical)=
=20
solution to this, not of the form
x=3D(some combination of basic functions).
y=3D(some combination of basic functions).
I'd suggest a numerical approach, such as bisection (or something that=20
converges a little faster) to get a number with whatever accuracy you want.
Try to find the zero crossing point of 1-x*x-sin(x) in whatever region you=
=20
want (there will be more than one solution, one positive, one negative I=20
think).
Cheers,
Roy Ward.
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