Is there a way to envision these two equations in spherical coordinates without plotting a bunch of points? I'm interested in what the surfaces look like.
$$\rho=\sin\theta\sin\phi$$
$$\rho^2(\sin^2\phi\sin^2\theta+\cos^2\phi)=9$$
2026-03-26 18:57:51.1774551471
Envisioning Spherical Coordinates
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I will assume $\theta$ is the azimuthal angle and $\phi$ the polar angle. By definition, then, $\sin\theta\sin\phi$ is just the spherical coordinate version of $y/\rho$. So the first equation is just $y=\rho^2=x^2+y^2+z^2,$ which is just a sphere (what is the center and radius?). For the second equation we instead obtain $y^2+z^2=9$. Do you recognize this figure?