My multivariable calculus HW question is to describe the plane $z=2$ in terms of spherical coordinates $(\rho,\vartheta,\varphi)$ and eventually write the equation as $\rho = f(\vartheta,\varphi)$.
I understand that $0≤\rho≤+\infty$ and $0≤\vartheta≤2π$ (I believe?). But I am having trouble determining the range of values of $\varphi$.
I know it cannot be all values between $0$ and $π$, because those spherical coordinates would just describe the entire space. I also know that $\varphi=\arccos(z/\rho)$ but I'm not sure what to do with that since $\rho$ can be anything.
Anyone know my next step? I can't find anything on cartesian planes in terms of spherical coordinates ):
Since, in spherical coordinates, $z=\rho\cos\phi$, the plane $z=2$ is, when expressed in spherical coordinates, the plane $\rho=\frac2{\cos\phi}=2\sec\phi$.