Rectangular and Polar Coordinates

Any quantity that has two components, can be represented in at least two different ways:

1. Rectangular Coordinates, where the magnitude of the components, can be represented by a point, with respect to a pair of orthogonal coordinate axes.
2. Polar Coordinates, where the two components are the distance from a reference point, called the origin, and the angle between the line from the point to the origin, and a reference axis.

To compute the polar representation of a point (x,y):

1. Compute the magnitude as:
   
   \(M\;=\;\sqrt{(x-0)^2+(y-0)^2}\)
   
   
2. Compute the angle as:
   
   \(\angle\;=\;tan^{-1} \left (\frac{y}{x} \right )\)

To invert the process, given a Magnitude, M, and an angle θ

1. Compute the x coordinate as:
   
   \(x\;=\;M\cdot cos(\theta)\)
   
   
2. Compute the y coordinate as:
   
   \(y\;=\;M\cdot sin(\theta)[\)