http://i56.tinypic.com/rtkmir.png

Polar points in space

A point in space can be determined by its' polar coordinates.

On the figure above, P's polar coordinates are $\displaystyle (\rho,\phi,\varphi)$.

$\displaystyle \rho$ is the lenght |OP|. $\displaystyle \phi$ is the angle between the z-axe and the line OP, and $\displaystyle \varphi$ is the angle between the x-axes and the line OQ.

Two areas in the space is given by polar coordinates:

$\displaystyle A={(\rho,\phi,\varphi)|1 \leq \rho \leq 3, Pi/4 \leq \phi \leq Pi/3, 0 \leq \varphi \leq 3Pi/4$

$\displaystyle B={(\rho,\phi,\varphi)|2 \leq \rho \leq 4, Pi/4 \leq \phi \leq Pi/2, - Pi/4 \leq \varphi \leq Pi/4$

Find a parametrization for A and B and $\displaystyle A \cap B$

I'm so lost in this, I would really appreciate any help (Doh)