 Because there are often many different possible coordinate systems for describing geometrical figures, it is important to understand how they are related.Such relations are described by "coordinate transformations" which give formulas for the coordinates in one system in terms of the coordinates in another system.For example, in the plane, if Cartesian coordinates ("x", "y") and polar coordinates ("r", "θ") have the same origin, and the polar axis is the positive "x" axis, then the coordinate transformation from polar to Cartesian coordinates is given by "x" = "r" cos"θ" and "y" = "r" sin"θ".