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Converting A Polar Equation to Rectangular Form

  1. Jul 22, 2010 #1
    1. The problem statement, all variables and given/known data
    Convert the polar equation to rectangular form.


    2. Relevant equations

    3. The attempt at a solution

    I can expand this out to


    multiply both sides by r




    Then I could expand the 2θ and get


    I'm not sure where to go from here.

    Plugging it into [tex]x^2+y^2=r^2[/tex] from here dosen't seam to help.

    The answer is supposed to be: [tex](x^2+y^2)^2=6x^2y-2y^3[/tex]
  2. jcsd
  3. Jul 22, 2010 #2


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    Homework Helper

    From here I would go ahead and distribute the 2, and then use the double-angle identities. For cosine, use the cos 2θ = cos2 θ - sin2 θ variant, like you did later on.

    After simplifying (you'll be able to combine like terms along the way), multiply both sides by [tex]r^3[/tex] instead of [tex]r[/tex], so that each trig function on the right side can be "paired" with an r. You will eventually be able to get to the answer you posted.

  4. Jul 22, 2010 #3


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    Homework Helper

    Use the expressions x=r cosθ, y=r sinθ.

  5. Jul 22, 2010 #4
    Ahhh.. yes.

    Thank you, that was a big help.

    Cant believe I didn't see that before.
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