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 Post subject: Iterative scheme to arrive at a solution?Posted: Fri, 24 Apr 2009 21:04:37 UTC
 S.O.S. Newbie

Joined: Tue, 21 Apr 2009 21:10:30 UTC
Posts: 1
Good readers, I wish to find a value for Y given any value of X for the equation:

acos(Y/((X^2+Y^2)^.5))+atan((Y-X)/(Y+X))-pi/4=0

How can this be done? I have tried and failed to use a ten year old Hewlett Pakard 48SX in equation solving mode to solve for Y given any value of X.

Are there any other calculators that can do this? Can someone recommend a course of action to solve this equation? Can the solution be graphed?

Am I correct in assuming that it can only be solved by some kind of iterative scheme?

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 Post subject: Re: Iterative scheme to arrive at a solution?Posted: Fri, 24 Apr 2009 22:00:28 UTC
 Senior Member

Joined: Fri, 9 Nov 2007 00:04:38 UTC
Posts: 128
Jeff Byram wrote:
Good readers, I wish to find a value for Y given any value of X for the equation:

acos(Y/((X^2+Y^2)^.5))+atan((Y-X)/(Y+X))-pi/4=0

How can this be done? I have tried and failed to use a ten year old Hewlett Pakard 48SX in equation solving mode to solve for Y given any value of X.

Are there any other calculators that can do this? Can someone recommend a course of action to solve this equation? Can the solution be graphed?

Am I correct in assuming that it can only be solved by some kind of iterative scheme?

Try

Your equation holds identically (it's true for all X and Y).
We have

Moving the pi/4 to the other side and taking the tangent of the equation yields

The addition formula for tangent is . Remembering that trig functions are nothing but ratios: if , then and so .

Now plugging this back into your equation yields , so we finally get 1=1.

_________________
"The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalize all those people."

Some people live their lives by the KISS principle (Keep It Simple Stupid), but I prefer a slightly different one:
Make It Fun And Complicate It Further, or MIFACIF. Ever try and find the volume of a cube in spherical coordinates?

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