## 3.6 Polar Coordinates

**A 2-vector (x, y) can be described by two numbers that are not coefficients
in a sum: its length, and the angle its vector makes with the x axis.**

The first of these is usually written as r, the second as .

**These parameters obey **

the inverse relations are

r and
are called polar coordinates.

Calculating the angle
in polar coordinates is a bit tricky; the obvious thing to try is atan(y, x)
but that is defined only between and
,
while
has a domain of size 2.

Here is something that works:

This gives theta in the range -
to .
If you want it to have range 0 to 2
you can add if(y < 0,8 * atan(1), 0) to it.