How to find how many intersections in a graph?

I made this graph that focuses only on the first quadrant. I am supposed to display the number of intersections between the circle and the tangent and negative cotangent graphs, and I am stuck at this very point. Any help here is deeply appreciated!

%Constant
r=4
dx=0.01

%Ranges
x1 = 0:pi/100:5*pi/2-dx;
x2 = 0:pi/100:5*pi/2-0.01;
x3 = 0:pi/100:5*pi/2-0.01;
%Function
tanFunc=@(x) tan(x)
cotFunc=@(x1) -cot(x1)
circleFunc = @(x3) sqrt(16-x3.^2);

diff_fun = @(v) circleFunc(x2) - tanFunc(x3);

%Plotting
y1=tanFunc(x1)
hold on
y2=cotFunc(x2)
hold on
y3=circleFunc(x3)
%plot(x2, y2)
plot(x1, y1, x2, y2, x3, y3)

%Graph Addon
set(gca,'XLim',[0 r]);
set(gca,'YLim',[0 r]);

Answer 1

[KSSV]

Refer this function:

https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections

[Philip Chen]

Thanks. I found all of the intersections, but I want the program to display HOW MANY intersections that it found.

[KSSV]

You caclulate the dimensions of the output from interX. I guess output of intersetion points is a row matrix.

N = size(P,2)

Number of columns should give you number of intrsection points.