The easiest of representation in mathematics (of course in the 3D world) is Spherical Polar coordinates. But we use Cartesian coordinates everytime. Yes! It is fair to use ten,as we can imagine and calculate easily. But,in experience and usage,its the spherical coordinates which is ore specific and theoretical in sense.
This usage of Cartesian coordinates originated back from the eras,when mechanics were initially studied. I can’t say,it the era of Newton,but his era is also one of them.
We can reason the usage with one of the greatest newton’s explanation : On Inertia.
Newton’s Law of inertia stated that,excluding all the external forces,a body executes equal intervals of displacements in equal intervals of time. Or there is a constant velocity for every body. It could either be zero or a positive value.
Even though,he assumed the Absoluteness of space and time,I doesn’t bother here much.
However,the first law,implied that space’s characteristics is same.
Space’s Characteristics won’t change with respect to the location. The Space is HOMOGENOUS.
Direction of properties in space doesn’t change these characteristics in space. The Space is Isotropic.
This two concepts of Space : Homogeneity and the Isotropy,made it more user friendly for physicists to use Rectangular Cartesian coordinates.
Das Cartesian Coordinates!