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#1 2005-07-22 10:38:42

GurraTedden
Member
Registered: 2005-07-20
Posts: 19

equations, equations...

This suddenly felt impossible:
How do I transform these three equations...

(1): xz=bc
(2): cos(y) + xsin(y)=0
(3): zsin(y) + xzcos(y) - c(a+b)=0
(three unknown x,y,z with three equations, always solvable right!? But i only want to solve this for x!!!)
(I've looked it through carefully, so it shouldn't be any errors in there)

...to either of these too:
answer, version1: x=1/√((a/b+1)²-1)
          , version2: x=tan(arcsin(b/(a+b))

This is how far I've got:
(1) can be rewritten to: x=bc/z            , new(4)
(2)        -"-                : x=cos(y)/sin(y)              , new(5)
(3)        -"-                : z=c(a+b)/(sin(y)+xcos(y))             ,new(6)

(6) in (4) --> x=b(sin(y)+xcos(y))/(a+b)               , new(7)
(5) in (7) --> cos(y)/sin(y)=b(sin(y)+cos²(y)/sin(y))/(a+b) --> [multiplying both sides with sin(y)] cos(y)=b/(b+c)

So, finally: I'm getting y=arccos(b/(a+b)), BUT HOW DO I PROCEED... It's a dead end. I don't know what more to do...
Maybe you do?

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#2 2005-07-22 10:49:33

GurraTedden
Member
Registered: 2005-07-20
Posts: 19

Re: equations, equations...

CORRECTION: eq(2) should be: cos(y) - xsin(y)=0!

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#3 2005-07-22 16:55:44

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,892

Re: equations, equations...

GurraTedden wrote:

(three unknown x,y,z with three equations, always solvable right!? But i only want to solve this for x!!!)

There are actually six variables...x,y,z,a,b,c roll


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#4 2005-07-22 19:01:25

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: equations, equations...

Yes, but he can measure a, b and c, so he wants to make x the subject of an equation involving just those.


Why did the vector cross the road?
It wanted to be normal.

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