Relation between polar coordinate system and Cartesian system

A frequently utilized non-cartesian system is Polar coordinate system. The subsequent figure A demonstrates a polar coordinate reference frame. Within polar coordinate system a coordinate position is identified via r andq, here r is a radial distance from the coordinate origin and q is an angular displacement from the horizontal as in figure 2A. Positive angular displacements are counter clockwise. Angle q is measured in degrees. One full counter-clockwise revolution regarding the origin is treated as 360⁰. A relation among Cartesian and polar coordinate system is demonstrated in Figure 2B.

Figure: A polar coordinate reference-frame          Figure 2B: Relation between Polar and Cartesian coordinates

Consider a right angle triangle in Figure B. By utilizing the description of trigonometric functions; we transform polar coordinates to Cartesian coordinates:

x=r.cosθ

y=r.sinθ

 The opposite transformation from Cartesian to Polar coordinates is:

 r=√(x²+y²) and θ=tan^-1(y/x)