To establish polar coordinates on a plane, we choose a point #O# - the origin of coordinates, the pole, and a ray from this point to some direction #OX# - the polar axis (usually drawn horizontally).
Then the position of every point #A# on a plane can be defined by two polar coordinates: a polar angle #varphi# from the polar axis counterclockwise to a ray connecting the origin of coordinates with our point #A# - angle #/_ XOA# (usually measured in radians) and by the length #rho# of a segment #OA#.
To graph a function in polar coordinates we have to have its definition in polar coordinates.
Consider, for example a function defined by the formula
#rho=varphi# for all #varphi>=0#.
The function defined by this equality has a graph that starts at the origin of coordinates #O# because, if #varphi=0#, #rho=0#.
Then, as a polar angle #varphi# increases, the distance from an origin #rho# increases as well. This gradual increase in both polar angle and distance from the origin produces a graph of a spiral.
After the first full circle the point on a graph will hit the polar axis at a distance #2pi#. Then, after the second full circle, it will intersect the polar axis at a distance #4pi#, etc.
