who came up with the system?
Grégoire de Saint-Vincent and Bonaventura Cavalieri
Polar coordinate system
Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-seventeenth century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th-century. 
when are polar coordinates used in real life In spirals
wiki:25628468
Polar coordinate system [SEP] Introduction
Angles in polar notation are generally expressed in either degrees or radians (2 rad being equal to 360°). Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-seventeenth century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th-century. The initial motivation for the introduction of the polar system was the study of circular and orbital motion. Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. Planar physical systems with bodies moving around a central point, or phenomena originating from a central point, are often simpler and more intuitive to model using polar coordinates.