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Homework Help: Graphing in spherical coordinates

  1. Nov 9, 2011 #1
    1. The problem statement, all variables and given/known data

    The question involves a triple integral, but I can figure that out once I know what this looks like visually. It is the graph of ρ = 1 + cos(∅)
    How exactly would I graph this?

    2. Relevant equations

    x = ρ * sin(∅) * cos(θ)
    y = [itex]\rho[/itex] * sin(∅) * sin(θ)
    z = ρ * cos(∅)

    3. The attempt at a solution

    I don't really know where to start. I tried converting to Cartesian because it wasn't something that was easy to visualize for me in spherical, but that was a mess. Would it be a torus? I only vaguely know what that is. I apologize, we just learned this stuff today! I want to make sure that I am solid on it.
  2. jcsd
  3. Nov 10, 2011 #2


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    Gold Member

    Well, as you have discovered, you aren't going to get a nice simple xyz equation from which you will recognize the graph. One thing that you know for sure is that since there is no [itex]\theta[/itex] in the equation it is a surface of revolution around the z axis. So its cross section in, for example, the yz plane would tell you the shape.

    Think about what the polar coordinate graph of r = 1 + cos(θ) would look like. Do you know how you would graph that curve? Do you know what kind of curve it is?

    The reason I am asking you that is, when you look at the trace of your surface in the yz plane the [itex]\rho,\phi[/itex] pair look just like polar coordinates off the z axis. So if you can figure out the shape of the polar curve, just rotate it up on the z axis and revolve it to get your surface. Come back if you have more questions.
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