plotting a surface using cylindrical co-ordinates

Question

I need to plot the following surface :

phi=45 degree 0

My only problem is with this constant phi, I can't know how to represent a surface with constant phi.

Answer 1

If all you have is $\phi = 45^{\circ}$, then this defines a closed half-plane perpendicular to the plane $z=0$, passing through the ray $x=y$ with $x$ and $y$ positive. Here, $\rho$ and $z$ can be anything.

If you have, for example, $\phi = 45^{\circ}, \rho = \sqrt{2}$, then this is a line perpendicular to the $z=0$ plane, and passing through $(x,y)=(1,1)$. The coordinate $z$ can be anything.

If you have, for example, $\phi = 45^{\circ}, \rho = z$, then this is a ray starting from the origin and going through $(x,y,z) = (1,1,1)$.

Hope this helps.