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Polar to Rectangular conversions

  1. Feb 16, 2006 #1
    I am at a standstill with the solution to this problem.

    I need to convert r^2=2cos(2 theta) to rectangular form.

    I know that x = rcos(theta) and y = rsin(theta)

    so far I have r = (2cos(2theta))/r

    then I substitute for r

    sqrt(x^2+y^2)= (2cos(2theta))/sqrt(x^2+y^2)

    Then I hit a brick wall.

    please help me knock down this wall.

  2. jcsd
  3. Feb 16, 2006 #2


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    Homework Helper

    Replace r² by x²+y² and theta = arctan(y/x).
  4. Feb 16, 2006 #3
    So I then would have

    sqrt(x^2+y^2)= (2cos(2arctan y/x))/sqrt(x^2+y^2)

    I am still stuck.
  5. Feb 16, 2006 #4


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    Science Advisor

    Back up a little! You have [itex]r^2= 2 cos(2\theta)[/itex] so first note that [itex]cos(2\theta)= cos^2(\theta)- sin^2(\theta)[/itex] so that
    [itex]r^2= 2(cos^2(\theta)- sin^2(\theta))[/itex]
    Now multiply on both sides by r2 to get
    [itex](r^2)^2= 2(r^2cos^2(\theta)- r^2sin^2(\theta))[/itex]
    I'll bet you can convert that to rectangular coordinates!
  6. Feb 16, 2006 #5

    This is now so simple.
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