How can you find the x intercepts between two signals in Matlab

Hello! So I am plotting two different signals in Matlab that have a few intercepts that I would like to find. How can I have Matlab find and spit out these values for me? I tried find (faa1 == faa2) but it returned nothing. Here is my code:

if true
  aa = 0:.0001:4*pi;
  faa1 = ((12.*sin(aa))./aa) + cos(aa);
  faa2 = cos(aa);
  plot(aa,faa1), grid on
  hold
  plot(aa,faa2)
end

Answer 1

[Star Strider]

See if this does what you want:

aa = 0:.0001:4*pi;
faa1 = ((12.*sin(aa))./aa) + cos(aa);
faa2 = cos(aa);

faad = faa1 - faa2;                         % Subtract Functions
shiftmult = faad.*circshift(faad, [0 -1]);  % Detect Zero-Crossings
xzc = find(shiftmult <= 0);                 % Find Incides Of Zero-Crossings
xint = aa(xzc)                              % X-Intercepts

plot(aa,faa1), grid on
hold on
plot(aa,faa2)
plot(aa(xzc), faa2(xzc), 'bp')              % Plot Intersections
hold off

xint =
     3.1415     6.2831     9.4247