Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
  Transformation from spherical to cartesian :
  Using the expression for $\vec r$ in terms of cartesian basis, it is seen that
 
\begin{eqnarray*} x &=& r\sin\theta\cos\phi\\ y &=& r\sin\theta\sin\phi\\ z&=& r\cos\theta \end{eqnarray*}
  and the inverse transformation
 
\begin{eqnarray*} r &=& \sqrt{x^2+y^2+z^2}\\ \theta &=& \tan^{-1}\frac{\sqrt{x^2+y^2}}{z}= \cos^{-1}\frac{z}{r}\\ \phi &=& \tan^{-1}\frac{y}{x} \end{eqnarray*}
  Range of the variables are as follows :
 
\begin{displaymath}0\le r<\infty\ \ \ 0\le\theta\le\pi\ \ \ 0\le\phi\le 2\pi\end{displaymath}
   
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