The following information is found HERE
According to Daniel L. Klaasen in Historical Topics for the Mathematical Classroom:
Isaac Newton was the first to think of using polar coordinates. In a treatise Method of Fluxions (written about 1671), which dealt with curves defined analytically, Newton showed ten types of coordinate systems that could be used; one of these ten was the system of polar coordinates. However, this work by Newton was not published until 1736; in 1691 Jakob Bernoulli derived and made public the concept of polar coordinates in the Acta eruditorum. The polar system used for reference a point on a line rather than two intersecting lines. The line was called the "polar axis," and the point on the line was called the "pole." The position of any point in a plane was then described first by the length of a vector from the pole to the point and second by the angle the vector made with the polar axis.
According to Smith (vol. 2, page 324), "The idea of polar coordinates seems due to Gregorio Fontana (1735-1803), and the name was used by various Italian writers of the 18th century."
"Polar co-ordinates" is found in English in 1816 in a translation of Lacroix’s Differential and Integral Calculus: "The variables in this equation are what Geometers have called polar co-ordinates" (OED2).