% rigid boundary

figure(1)
theta = -pi/2:.01:pi/2;
kdover2 = .4;
kdover2 = .8;
kdover2 = 1.6;
kdover2 = 3.2;

plot(theta / pi * 180, abs(cos(kdover2 * cos(theta))))
xlabel('theta (degrees)')
ylabel('abs(cos(kdover2 * cos(theta)))')
v = axis;
v(1) = -90;
v(2) = 90;
v(3) = 0;
axis(v)
fix_axis
grid

figure(2)
rho = ones(size(theta));
polar(theta, abs(cos(kdover2 * cos(theta))))
fix_axis

% pressure release boundary

figure(3)
plot(theta / pi * 180, abs(sin(kdover2 * cos(theta))))
xlabel('theta (degrees)')
ylabel('abs(sin(kdover2 * cos(theta)))')
v = axis;
v(1) = -90;
v(2) = 90;
v(3) = 0;
v(4) = 1;
axis(v)
fix_axis
grid

figure(4)
rho = ones(size(theta));
polar(theta, abs(sin(kdover2 * cos(theta))))
fix_axis