Conversion between Cartesian and Polar Coordinates in Plane/Examples/(-2, -pi over 4)

Example of Use of Conversion between Cartesian and Polar Coordinates in Plane
The point $P$ defined in polar coordinates as:
 * $P = \polar {-2, -\dfrac \pi 4}$

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

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.