The value range of 1. polar coordinate r is to make two tangents of this area function image through the origin in rectangular coordinate system, and the included angle between these two tangents is the value range of θ in polar coordinate system. Then, in the rectangular coordinate system, the functional relationship about x and y is known to represent the range. Replace x_+y_ with r_, x with rcosθ, and y with rsinθ, and you can get the range of r.

2. Polar coordinate belongs to two-dimensional coordinate system, which was founded by Newton and is mainly used in the field of mathematics. Polar coordinate refers to taking a fixed point O on the plane, called the pole, drawing a ray Ox, called the polar axis, and then choosing a length unit and the positive direction of the angle (usually counterclockwise). 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.