For any point m on the plane, ρ represents the length of line segment om (sometimes R), θ represents the angle from Ox to OM, ρ is the polar diameter of point M, θ is the polar angle of point M, and the ordered number pairs (ρ, θ) are the polar coordinates of point M, so the established coordinate system is called polar coordinate system.

An important feature of the extended data polar coordinate system is that any point in the plane rectangular coordinate system can have infinite expressions in the polar coordinate system. Generally speaking, the point (r, θ) can be arbitrarily expressed as (r, θ 2kπ) or (? R, θ (2k+ 1) π), where k is an arbitrary integer. If the r coordinate of a point is 0, then no matter what value θ takes, the position of the point falls on the pole.

The curve equation described by polar coordinate system is called polar coordinate equation, which is usually used to indicate that ρ is a function of independent variable θ.