Hi every one,
I'd like to get y = f (x) of the following equation:
1= sin(x) . sin(y) + cos(y).cos(x) + cos(x) - cos(y)
Thanks and I look forward to hearing from you.
Said
Posted by: David W. Cantrell
"said" <ghofi@microsoft.com> wrote:
> I'd like to get y = f (x) of the following equation:
> 1= sin(x) . sin(y) + cos(y).cos(x) + cos(x) - cos(y)
Some solutions in the requested form are
y = (2*n+1)*pi
and
y = x + 2*n*pi
where n is an integer.
Other solutions, not of the form y = f(x), are x = 2*n*pi.
All of the solutions above are easily verified.
David Cantrell
Posted by: said
Hi David,
Thanks a lot your solution is brillant but I still have probleme because if
I have:
cos(z) = sin(x)-sin(y) ......(1)
sin(z)=1+cos(y)-cos(x) .....(2)
so cos(z)=0 then z = (2*n+1)*PI/2
so z is independant of y and x and is fix
but physicaly is not (equation of mouvement).
hopefully you could understand me and you've got solution.
looking forward to hearing from you.
Said
"David W. Cantrell" <DWCantrell@sigmaxi.org> wrote in message
news:20040805130903.485$1G@newsreader.com...
> "said" <ghofi@microsoft.com> wrote:
>
> > I'd like to get y = f (x) of the following equation:
> > 1= sin(x) . sin(y) + cos(y).cos(x) + cos(x) - cos(y)
>
> Some solutions in the requested form are
>
> y = (2*n+1)*pi
>
> and
>
> y = x + 2*n*pi
>
> where n is an integer.
>
> Other solutions, not of the form y = f(x), are x = 2*n*pi.
>
> All of the solutions above are easily verified.
>
> David Cantrell
Posted by: David W. Cantrell
"said" <ghofi@microsoft.com> wrote:
> Hi David,
> Thanks a lot your solution is brillant but I still have probleme because
> if I have:
> cos(z) = sin(x)-sin(y) ......(1)
> sin(z)=1+cos(y)-cos(x) .....(2)
>
> so cos(z)=0 then z = (2*n+1)*PI/2
> so z is independant of y and x and is fix
> but physicaly is not (equation of mouvement).
> hopefully you could understand me and you've got solution.
> looking forward to hearing from you.
Unfortunately I don't understand why you "still have probleme". Maybe
someone else can help you.
David
> "David W. Cantrell" <DWCantrell@sigmaxi.org> wrote in message
> news:20040805130903.485$1G@newsreader.com...
> > "said" <ghofi@microsoft.com> wrote:
> >
> > > I'd like to get y = f (x) of the following equation:
> > > 1= sin(x) . sin(y) + cos(y).cos(x) + cos(x) - cos(y)
> >
> > Some solutions in the requested form are
> >
> > y = (2*n+1)*pi
> >
> > and
> >
> > y = x + 2*n*pi
> >
> > where n is an integer.
> >
> > Other solutions, not of the form y = f(x), are x = 2*n*pi.
> >
> > All of the solutions above are easily verified.
> >
> > David Cantrell
Posted by: said
Hi ,
I 'd like to get just z = f(x) or z = f(y) of the following equations:
cos(z) = sin(x)-sin(y) ......(1)
sin(z)=1+cos(y)-cos(x) .....(2)
Thanks
Said
Posted by: said
Hi,
I'd like to get just z = f(x) or z = f(y) of the following equations:
cos(z) = sin(x)-sin(y) ......(1)
sin(z)=1+cos(y)-cos(x) .....(2)
Thanks
Said
Posted by: Bill Rogers
On Fri, 6 Aug 2004 14:06:19 +0100, "said" <ghofi@microsoft.com> wrote:
>Hi ,
>I 'd like to get just z = f(x) or z = f(y) of the following equations:
> cos(z) = sin(x)-sin(y) ......(1)
> sin(z)=1+cos(y)-cos(x) .....(2)
>Thanks
>Said
I may be wrong, but you are seemingly asking either in the original
and this message for a *simple8 analytic separation of variables, y as
a function of x, and it's not possible as far as I know. If you
expressed sine functions in terms of cosine, you'd still wind up with
an equation involving cos(x) and cos(y) which is not readily
separable, there being second degree variants [cos(x) cos(y),
cos^2(x)cos(y) and so on]... .
Where do you find such a question?
Bill.
Posted by: said
Hi bill
thanks vry much indeed.
Posted by: Julien Cassaigne
Said <ghofi@microsoft.com> demande :
>I'd like to get y = f (x) of the following equation:
>1= sin(x) . sin(y) + cos(y).cos(x) + cos(x) - cos(y)
Voici un indice : essaie d'exprimer ton équation en fonction
de sin((x+y)/2) et sin((x-y)/2), en utilisant les formules
classiques de trigonométrie (cos(a)-cos(b), cos(a-b), cos(2a)).
À l'arrivée l'équation se factorise et on trouve trois familles
de solutions (et on est sûr qu'il n'y en a pas d'autres).
y = x + 2 n pi
y = pi + 2 n pi
x = 2 n pi
Julien.
Posted by: said
Hi Julien,
I 'd like to get just z = f(x) or z = f(y) of the following equations:
cos(z) = sin(x)-sin(y) ......(1)
sin(z)=1+cos(y)-cos(x) .....(2)
Thanks
Said
Posted by: said
Hi Bill,
j'ai besoin de ces equations pour avoir une animation ( dans 3ds max ) de 3
elements lies entre eux par ces trois equations (x,y et z sont des angles)
autrement dis ce sont des equations de mouvement d'un systeme de 3 elements
..
disant que x=2*pi*t /T telle que T est la periode et t est le temps.
donc le premier element a un mouvement de rotation
mais les equations de mouvemet de y et z ?