Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
  Relationship with the cartesian components are
 
\begin{eqnarray*} x&=& \rho\cos\theta\\ y&=& \rho\sin\theta \end{eqnarray*}
  so that the inverse relationships are
 
  By definition, the distance $\rho>0$. we will take the range of angles $\theta$ to be $0\le\theta<2\pi$ (It is possible to define the range to be $-\pi\le\theta<+\pi$). One has to be careful in using the inverse tangent as the arc-tan function is defined in $0\le \theta<\pi$. If $y$ is negative, one has to add $\pi$ to the principal value of $\theta$ calculated by the arc - tan function so that the point is in proper quadrant.
  Example 2
   
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