What does coordinate mean in math terms?

Answer 1

Literally, "Values that Ordain Together" the location of the point in question.

On a 2-dimensional Cartesian graph it is (x, y) where x & y are values counting along their respective axes. So (4, 2) means go along the x-axis 4 units from the origin (0, 0,) then up 2 units "y-wards".

In 3 dimensions we add z to the list to mean x & y are horizontal and the z values go up (or down, like investments!). So (x, y, z)

A good example is a hill-top altitude on a map having a grid system: z is then the hill's altitude.

Some of the more wayward Microsoft 'Excel' graph options make heavy use of this system to produce plots that are more art than maths, generally to impress business types who are no cleverer than they should be! Used intelligently though, 3D or (x,y,z) co-ordinates have a multitude of uses in science, engineering & computer programming.

In polar graphs the co-ordinates are (angle, radial-value), where the angle may be degrees or radians.

I've not heard of spherical-angle co-ordinates but I dare say they can exist: go round x-degrees, inwards y-units, up z-units.