What is the difference between a rectangular coordinate system and a polar coordinate system?

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What is the difference between a rectangular coordinate system and a polar coordinate system?

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Answer 1 · 2015-03-26T04:10:03

One of the most interesting differences is that every point in the plane has exactly one representation as a pair of coordinates in the rectangular (or any other parallelogram) coordinate system, but has infinitely many representations in polar coordinates.

Example:

The point whose rectangular coordinates are $(1, 1)$ $(1,1)$ corresponds to polar coordinates:
$(\sqrt{2}, \frac{π}{4})$ $(sqrt2, pi/4)$ and also $(\sqrt{2}, \frac{9 π}{4})$ $(sqrt2, (9 pi)/4)$ and $(\sqrt{2}, \frac{- 7 π}{4})$ $(sqrt2, (-7 pi)/4)$ and $(- \sqrt{2}, \frac{5 π}{4})$ $(-sqrt2, ( 5 pi)/4)$ and infinitely many others.

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What is the difference between a rectangular coordinate system and a polar coordinate system?

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