1 coordinate systems

in 3 dimensions

Let P be a point in the given coordinate system

1.1 rectangular

P = (x, y, z)

1.2 cylindrical

P = (\rho, \phi, z)

1.3 spherical

P = (r, \theta, \phi)

1.4 bridge between systems

• rectangular \leftrightarrow cylindrical

\begin{matrix} x &=& \rho \cos \phi \\ y &=& \rho \sin \phi \\ z &=& z \\ \end{matrix}

• rectangular \leftrightarrow spherical

\begin{matrix} x &=& r \sin \theta \cos \phi \\ y &=& r \sin \theta \sin \phi \\ z &=& r \cos \theta \\ \end{matrix}

• cylindrical \leftrightarrow spherical

\begin{matrix} \rho &=& r \sin \theta \\ \phi &=& \phi \\ z &=& r \cos \theta \\ \end{matrix}