Having issues plotting and coloring Limacon

This is the problem im having an issue with: PLEASE DO NOT GIVE OR DO THE PROBLEM FOR US

"the curve given in polar coordinates by r = 1 − 2 sin θ. This curve has an inner loop and an outer loop. Plot the inner loop in green and the outer loop in magenta. You may not use Matlab’s commands polar or polarplot or anything similar. "

we would like to know how to find the equation for just the inner loop and not the entire loop that includes both the inner and outer parts, and any hints on how you would personally go about coloring the different sections

what we have rn, its ugly we know;

th = 0 : pi/100 : 2*pi;
th2 = pi/6 : pi/100: 5*pi/5.91;
r = 1 - 2*sin(th);
x_3 = r.*cos(th);
y_3 = r.*sin(th);

r2 = 1 - 2*sin(th2);
x_4 = r.*cos(th2);
y_4 = r.*sin(th2);

figure()
plot(x_3, y_3, 'm')
hold on
plot(x_4, y_4, 'g')
xlabel('X = r*cos(\theta)');
ylabel('Y = r*sin(\theta)');
title('Plot of r = 1 - 2*sin(\theta)');
grid on

One of the problems we found, is while it looks right, the graphs arent producing the same curve.

Thank you any hints and input is appreciated.

Answer 1

[Star Strider]

You already have most of it done, and correctly, so congratulations!

You need to keep the ‘r’ and ‘th’ calculations together, as well as the ‘r2’ and ‘th2’ calculations, because ‘th’ and ‘th2’ are different lengths, so mixing them will cause problems:

r = 1 - 2*sin(th);
x_3 = r.*cos(th);
y_3 = r.*sin(th);
r2 = 1 - 2*sin(th2);
x_4 = r2.*cos(th2);
y_4 = r2.*sin(th2);

The only hint you need otherwise is to duplicate your two plot calls, although instead of using plot in the duplicates, use the fill (link) function, so:

plot(a,b,,'r')
fill(a,b,'r')  

for each.