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Coordenadas esféricas

\begin{figure}\centerline{\epsfig{file=Coord_Esfer.eps,width=12cm}}\end{figure}

Relação com coordenadas cartesianas:

$\displaystyle {\color{myblue}x \, = \, r \, {\rm sen} \phi \, {\rm cos} \theta}
\quad$ $\textstyle ,$ $\displaystyle \quad
r \, = \, \sqrt{x^2 \, + \, y^2 \, + \, z^2}$  
$\displaystyle {\color{myblue}y \, = \, r \, {\rm sen} \phi \, {\rm sen}\, \theta}
\quad$ $\textstyle ,$ $\displaystyle \quad
{\rm sen} \theta \, = \, y/\sqrt{x^2+y^2}$  
$\displaystyle {\color{myblue}z \,= \, r \, {\rm cos} \phi \quad} \;
\quad \quad$ $\textstyle ,$ $\displaystyle \quad
{\rm cos} \theta \, = \, x/\sqrt{x^2+y^2}$  
    $\displaystyle \quad
{\rm cos} \phi \, = \, \frac{z}{r} \, = \, \frac{z}{\sqrt{x^2+y^2+z^2}}$  



Luis Raul Weber Abramo 2002-08-08