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Intersection pts of polar equations

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data
    I have to find the area of the region that lies inside the curves:

    r = sin(θ)
    r = sin(2θ)

    3. The attempt at a solution

    I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each other:

    sin(θ) = sin(2θ)

    arcsin both sides:
    θ = 2θ

    And I'm stuck. Analysis of the graph shows that the most crucial intersection point occurs at or very close to 75º, but I would like to be able to show that.
  2. jcsd
  3. Mar 13, 2010 #2


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    Homework Helper

    Taking arcsin of both sides will only give you some solutions. Try using sin(2x)=2*sin(x)*cos(x).
  4. Mar 13, 2010 #3
    Thanks a lot! In that case...

    sin(θ) = 2sin(θ)cos(θ)
    1 = 2cos(θ)
    cos(θ) = 1/2
    θ = π/3

    That should help me get the rest of the problem, thanks again! =]
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