What Are Polar Coordinates?

Polar coordinates belong to a two-dimensional coordinate system. The founder is Newton, which is mainly used in the field of mathematics. Take a fixed point O in the plane, called the pole, and draw a ray Ox , called the polar axis, and then select a length unit and the positive direction of the angle (usually taken counterclockwise). For any point M in the plane, is the length of the line segment OM (sometimes also expressed by r), is the angle from Ox to OM , is the pole diameter of point M , is the pole angle of point M , and the ordered number pairs (, ) is called the polar coordinate of the point M , and the coordinate system thus established is called the polar coordinate system. In general, the polar coordinate unit of M is 1 (length unit), and the polar coordinate unit is rad (or °).

As we all know, the Greeks first used the concepts of angle and radian. astronomer

The crossing point M is taken as the vertical line of the axis Ox .

. Vector

Called vector

Polar projective vector, written as

. In a few cases, PrjPoint can also be described as a "projective point", and PrjVector can also be described as a projective vector.

In the polar coordinate system Ox , a plane Rt coordinate system xOy is established with O as the origin and Ox as the positive direction of the x- axis. Vector

= (, ), then ^[4]

The first to use polar coordinates to determine the position of a point on a plane is

How to represent points

Described in polar coordinate system

Planetary

According to the above formula, the double integral can be transformed from rectangular coordinates to polar coordinates, as follows: ^[6]