Because "circular-type" functions can be more easily described by the periodic functions 
and 
, which are deeply involved in the behavior of "circular-type" functions. Also, using a polar coordinate plane allows you to draw graphs of equations that typically aren't functions.
For example, the unit circle requires two equations to be graphed to fully represent the circle in the rectangular coordinate plane.
On the other hand, in polar coordinates, substituting
and 
reduces this to a constant function,
(since by definition, 
)
For example, the unit circle requires two equations to be graphed to fully represent the circle in the rectangular coordinate plane.
On the other hand, in polar coordinates, substituting