This drawing shows the relationship between descriptions of a vector r→{\displaystyle {\vec {\boldsymbol {r}}}} in the cartesian (x,y,z){\displaystyle (x,y,z)}, cylindrical (ρ,ϕ,z){\displaystyle (\rho ,\phi ,z)}, and spherical (r,θ,ϕ){\displaystyle (r,\theta ,\phi )} coordinate systems.  The symbols used here follow the convention in physics, which differs from that used commonly in mathematics textbooks.
en:Image:Physics Coordinates.png
en:User:Jacobolus, User:Stannered