Simply put; polar coordinates are used to show** how far away a point is and at what angle it is** so, for example, you have the length of a diagonal line (r)and the angle formed** `` ** between the x-axis and the point

(r;`theta` ).You would convert using the cos or sin function depending on what you need to find.

as opposed to what you are used to with **x and y coordinates** which measure** how far up** (on this graph 2) and **how far across**(4) rendering coordinates of (4;2).

Polar coordinates are used when solving for direction and length from a certain point. Some otherwise complicated calculations for curves are simplified using polar coordinates. Thus, they are used to show

**how far away a point is and at what angle it is**

In Cartesian or xy-plane points are written as (x,y) where as in polar coordinate system points are written as (r,`theta` ).

A relation between these two system is defined as

`x=r cos(theta)`

`y=r sin(theta)` `theta=tan^-1(y/x)` and `r=sqrt(x^2+y^2)`