How to locate all intersection points on a polar graph
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I am attempting to locate all four intersection points that occur on my polar graphs but Matlab is only returning 2 of the 4 when setting the graph equations equal to each other and asking it to evaluate the 2 graphs. Is there something different with polar graphs than linear graphs in how Matlab finds the intersection points? It returns the intersection points for Quadrant 2, but it doesn't return the result for Quadrant 3.
Here is my code.
close all;
clear;
clr;
syms x
r1 = ((cos(x))^2)+((sin(x))^2);
r2 = 2-(4*cos(x));
ezpolar(r2)
hold on;
grid on;
ezpolar(r1)
title('Polar Graph of r = 2 - 4*cos(theta) and r = 1')
legend('r = 2 - 4cos(theta)','r = 1')
Intersection = solve(r1==r2);
disp(['The two graphs intersect at the following values '])
disp(Intersection)
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