This is one application of polar coordinates, represented as (r, θ). (r, θ). we interpret r r as the distance from the sun and θ θ as the planet’s angular bearing, or its direction from a fixed point on the sun. in this section, we will focus on the polar system and the graphs that are generated directly from polar coordinates. Identify and graph polar equations by converting to rectangular equations. we have learned how to convert rectangular coordinates to polar coordinates, and we have seen that the points are indeed the same. we have also transformed polar equations to rectangular equations and vice versa.
On the polar grid, the equivalent of the positive x axis on the rectangular grid. polar coordinates. on the polar grid, the coordinates of a point labeled (r, θ), where θ indicates the angle of rotation from the polar axis and r represents the radius, or the distance of the point from the pole in the direction of θ. Some of the formulas that produce the graph of a circle in polar coordinates are given by [latex]r=a\cos \theta [ latex] and [latex]r=a\sin \theta [ latex], where [latex]a [ latex] is the diameter of the circle or the distance from the pole to the farthest point on the circumference. First, testing the equation for symmetry, we find that the graph of this equation will be symmetric about the polar axis. next, we find the zeros and maximums. setting r = 0 r = 0, we have θ = π 2kπ θ = π 2 k π. the zero of the equation is located at (0, π) ( 0, π). Example 1. testing a polar equation for symmetry. test the equation r = 2sin θ r = 2 s i n θ for symmetry. show hide solution. test for each of the three types of symmetry. 1) replacing (r,θ) ( r, θ) with (−r,−θ) ( − r, − θ) yields the same result. thus, the graph is symmetric with respect to the line θ =π 2 θ = π 2.
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