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Calculus 3 Problem (explain solution)

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Put the equation: p = 2 sin (x) cos (y) into rectangular coordinates. Identify the surface



    3. The attempt at a solution
    I tried to look at all the identities but I can't seem to figure out which one to use. I have the solutions to this problem, which follows:

    p^2 = 2 p sin x cos y
    => x^2 + y^2 + z^2 = 2x (Where did this come from?)
    => x^2 - 2x + y^2 + z^2 = 0
    => (x^2-2x+1) + y^2 + z^2 = 1, which is a sphere of axis (1,0,0)

    Can anyone explain the solution? Thank you
     
  2. jcsd
  3. Oct 18, 2009 #2

    LCKurtz

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    Apparently you are dealing with spherical coordinates and the variable you are calling p is actually the spherical coordinate usually denoted as [itex]\rho[/itex]. And, what's worse, the x and y in your equation also don't represent the cartesian x and y. Here's what I think your given equation should be:

    [tex]\rho = 2\sin(\phi)cos(\theta)[/tex]

    where [itex](\rho,\phi, \theta)[/itex] are the spherical coordinates of (x,y,z). Try following your argument knowing that and using the usual spherical coordinate formulas.
     
  4. Oct 18, 2009 #3
    You're right. That is supposed to be the right equation, but I just used x and y because I didn't understand how to use the symbols lol. I was/am browsing through my textbook and notes, but was unable to find to relate rho, phi, and theta to spherical coordinates. I understand that x^2 + y^2 and z^2 is the spherical formula, but I still don't understand the 2x portion.
     
  5. Oct 18, 2009 #4

    LCKurtz

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  6. Oct 18, 2009 #5
    Oh! I finally get it now lol. thank you
     
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