I want to ask that why did we need the polar and spherical coordinates when we had the rectangular coordinates to find out the positon of anything in 3-dimensional space.
For example, we use double and triple integration to find the area of a region under a surface, or the volume of a solid in 3D space. If that region is a circle or is composed of circles, or if the solid is a sphere or a hemisphere, then the integration becomes very complex and very nasty in rectangular coordinates, but if you change the problem into the polar domain, things become a lot easier, and the functions are elementary to integrate.
Cylindrical and spherical coordinates are used to exploit a certain geometry. In addition to the examples given above the classical is locating points (or cities) in the world. There are given by longitude and laditude. Why, because the world is essentiall spherical and longitude and laditude are two angles.