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2D Coordinates Systems

Tool to achieve coordinates system changes in the 2d-plane (cartesian, polar, etc.). These are mathematical operations representing the same elements but in different referentials.

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2D Coordinates Systems -

Tag(s) : Geometry

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2D Coordinates Systems

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Change of 2D Coordinates (plane)

Cartesian to Polar Coordinates



Polar to Cartesian Coordinates



Change of 3D Coordinates (space)

Answers to Questions (FAQ)

How to convert cartesian coordinates to polar?

The base / referential change using cartesian coordinates $ (x, y) $ to another referential using polar coordinates $ (r, \theta) $ obey the equations: $$ r = \sqrt{x^2 + y^2} \\ \theta = 2\arctan\left(\frac y{x+ \sqrt{x^2+y^2}} \right) $$ with $ \arctan $ the reciprocal of the function $ \tan $ (tangent).

NB: the value of $ \theta $ calculated here is included in the inverval $ ] -\pi, \pi] $ (to have it in the interval $ ] 0, 2\pi] $ add $ 2 \pi $ if the value of the angle is negative)

If $ r = 0 $ then the angle can be defined by any real number

Example: The point of the plane in position $ (1,1) $ in Cartesian coordinates is defined by the polar coordinates $ r = \sqrt {2} $ and $ \theta = \pi/4 $

How to convert polar coordinates to cartesian?

The base / referential change from polar coordinates $ (r, \theta) $ to another referential using cartesian coordinates $ (x, y) $ follows the equations: $$ x = r \cos (\theta) \\ y = r \sin (\theta) $$

with $ r $ a positive real number and $ \theta $ an angle defined between $ ] -\pi, \pi] $

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