An angle
and a positive real number
define a unique point
-
![{\displaystyle {}P=(x,y)=(r\cos \alpha ,r\sin \alpha )=r(\cos \alpha ,\sin \alpha )\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b59737f68f77105af21071019b07370a26aecdf1)
in the real plane
. Here,
is the distance between the point
and the zero point
and
means the intersecting point of the ray through
with the unit circle. Every point
has a unique representation with
and with an angle
, which has to be chosen accordingly
(the zero point is represented by
and an arbitrary angle).
The components
are called the polar coordinates of
.