Model C2: Converting Between Rectangular and Polar

Here are some conversions between 2D coordinate systems and between 3D coordinate systems.

RectToPolar[{x_,y_}]:={Sqrt[(x^2)+(y^2)],ArcTan[x,y]};
PolarToRect[{r_,θ_}]:={r*Cos[θ],r*Sin[θ]};

RectToSpherical[{x_,y_,z_}]:={Sqrt[(x^2)+(y^2)+(z^2)],ArcTan[x,y],ArcTan[Sqrt[(x^2)+(y^2)],z]};
SphericalToRect[{ρ_,θ_,ϕ_}]:={ρ*Cos[ϕ]*Cos[θ],ρ*Cos[ϕ]*Sin[ϕ],ρ*Sin[ϕ]};

CylindricalToRect[{r_,θ_,z_}]:={r*Cos[θ],r*Sin[θ],z};
CylindricalToRect[{r_,θ_,z_}]:=Flatten[PolarToRect[r,θ],z];

CylindricalToSpherical[{r_,θ_,z_}]:=RectToSpherical[CylindricalToRect[{r,θ,z}]];