You can convert from one coordinate system to another using the formulae below.
1. From 2D Cartesian to Polar
\[ \begin{array}{rcl}
r & = & \sqrt{x^2 + y^2} \\
\theta & = & \mathrm{atan2}(y, x) \\
\end{array}\]
where atan2 is an arc tangent function which takes into account the quadrant.
2. From Polar to 2D Cartesian
\[ \begin{array}{rcl}
x & = & r \cdot \cos(\theta) \\
y & = & r \cdot \sin(\theta) \\
\end{array}\]
3. From 3D Cartesian to Spherical
\[ \begin{array}{rcl}
r & = & \sqrt{x^2 + y^2 + z^2} \\
\theta & = & \mathrm{atan2}(z, x) \\
\phi & = & 90^\circ - \arccos(y/r) \\
\end{array}\]
where \(\theta\) corresponds to the azimuth angle and \(\phi\) to the elevation angle.
4. From Spherical to 3D Cartesian
\[ \begin{array}{rcl}
x & = & r \cdot \cos\theta \cdot \cos\phi \\
y & = & r \cdot \sin\phi \\
z & = & r \cdot \sin\theta \cdot \cos\phi \\
\end{array}\]
where \(\theta\) corresponds to the azimuth angle and \(\phi\) to the elevation angle.