How to represent points in euclidean space using polar coordinates? What other options are available to represent it?

Question

When we talk about Euclidean space or n-Euclidean space, using notations such as $\Bbb R^n$ or $\Bbb E^n$ which are basically n-tuples of real numbers and if distance function is to be added, then we can certainly call it a euclidean space (metric space). But that's just a sort of Cartesian space if we are using n-tuples for our purpose. Is there any way to represent it in polar coordinates and if not than why do we exempt from calling n-Euclidean space as Cartesian space when it's already evident that points here are represented as tuples of numbers (ordered pairs or ordered triple in context of 2-D and 3-D resp.).