Question

Suggest methods (other than Cartesian Coordinates) of describing the location of points on a plane.

Answer 1

There are two alternatives: (i) Polar coordinate system (a.k.a. Circular coordinate system), (ii) Elliptic coordinate system.

Explanation:

There are two alternative ways of describing the location of points on a plane:

(i) Polar coordinate system (a.k.a. Circular coordinate system).

(ii) Elliptic coordinate system.

Now we proceed to explain briefly the characteristic of each option:

Polar coordinate system:
`(r, \theta)`

Where:

`r` - Distance of the point with respect to origin.

`\theta` - Direction of the vector between origin and point with respect to the +x semiaxis, in sexagesimal degrees.

The formulae for each component in terms of Cartesian coordinates are described below:

`r = \sqrt{x^(2)+y^(2)}` (1)

`\theta = \tan^(-1) (y)/(x)` (2)

Elliptic coordinate system:
`(\mu, \\u)`

Where
`\mu` and
`\\u` are elliptical coordinates.

The formulae for each component in terms of Cartesian coordinates are described below:

`x = a\cdot \cosh \mu \cdot \cos \\u` (3)

`y = a \cdot \sinh \mu \cdot \sin \\u` (4)

Where
`a` is the distance between origin and any of the foci along the x axis.