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:

    \(y\;=\;M\cdot sin(\theta)[\)

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