Conversion between Cartesian and Polar Coordinates in Plane/Examples/(4, pi over 3)

Example of Use of Conversion between Cartesian and Polar Coordinates in Plane
The point $P$ defined in polar coordinates as:
 * $P = \polar {4, \dfrac \pi 3}$

can be expressed in the corresponding Cartesian coordinates as:
 * $P = \tuple {2, 2 \sqrt 3}$

Proof
Let $P$ be expressed in Cartesian coordinates as:
 * $P = \tuple {x, y}$

From Conversion between Cartesian and Polar Coordinates in Plane:

where in this case:

Hence:

and:

Hence the result.