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Very hard question about polar coordinates

  1. Jan 16, 2009 #1
    Hello, this question is about symmetry of polar coordinates.

    For a polar-curve to be symmetric around the x-axis we require that if (r,a) lies on the graph then (r,-a) or (-r,Pi-a) lies on the graph.

    To be symmetric about the y-axis we require that (-r,-a) or (r,Pi-a) lies on the graph.

    Now lets look at the graph r=cos(a/2)

    Since cos(-a/2)=cos(a/2) then the curve is symmetric about the x-axis. Of the requirements of symmetri I wrote earlier it doesn't seem to be symmetric about the y-axis. But when I draw it, symmetry about the y-axis occours. How can this be shown mathematically?

  2. jcsd
  3. Jan 16, 2009 #2

    D H

    Staff: Mentor

    The function in question obviously repeats over a range of 4*pi. What does the graph of the function over the range theta=0 to 2*pi versus theta=2*pi to 4*pi tell you about symmetry with respect to the y axis?
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