Graphing in spherical coordinates

[XcKyle93]

Homework Statement

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?

Homework Equations

x = ρ * sin(∅) * cos(θ)
y = $\rho$ * sin(∅) * sin(θ)
z = ρ * cos(∅)

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.

 

[LCKurtz]

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 $\theta$ 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 $\rho,\phi$ 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.