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Math Help - intersecting points - polar coordinates

  1. #1
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    intersecting points - polar coordinates

    Hi

    C1 r= 3cos x
    C2 r= 1 + cos x

    First question is find the polar coordinates of the intersection points of the two curves.

    I have found (3/2, pi/3) and (3/2, -pi/3) now what I am wondering is the point that we would normally consider (0,0) also an intersecting point and how would I find the coordinates for this point?

    Thanks

    Calculus beginner
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  2. #2
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    Quote Originally Posted by calcbeg View Post
    Hi

    C1 r= 3cos x
    C2 r= 1 + cos x

    First question is find the polar coordinates of the intersection points of the two curves.

    I have found (3/2, pi/3) and (3/2, -pi/3) now what I am wondering is the point that we would normally consider (0,0) also an intersecting point and how would I find the coordinates for this point?

    Thanks

    Calculus beginner
    Your question seems to be a bit unclear. (0, 0) is not in the solution set. In fact neither of your given curves passes through this point. As to the rest we have
    r = 3~cos( \theta)
    and
    r = 1 + cos( \theta)

    Since r = r this means
    3~cos( \theta) = 1 + cos( \theta)

    so
    2~cos( \theta) = 1

    cos( \theta ) = \frac{1}{2}

    You have mentioned the only two correct solutions. ( pi / 3 is the reference angle so there is another solution 4 pi / 3, or -pi / 3 which you already gave.

    -Dan
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