Why would you expect to find anything on this "message board" about this?!
I know nothing about this. But I
googled "cosine similarity example" (without quotes) and found a reference to an interesting discussion at
https://stackoverflow.com/questions...sine-similarity-in-a-very-simple-graphical-wa. The discussion includes a link to
http://www.miislita.com/information-retrieval-tutorial/cosine-similarity-tutorial.html#Cosim.
Combined with your wiki URL, I put together the following demonstration.
Suppose A1:A3 contains 1, 2, 3, and B1:B3 contains 4, -5, 6.
The following computes cos(theta) in C1, according to the wikipage:
=SUMPRODUCT(A1:A3, B1:B3) / SQRT(SUMSQ(A1:A3)) / SQRT(SUMSQ(B1:B3))
(Note that x/(y*z) = x/y/z.)
The result in C1 is 0.365486942323904. That rounds to 0.37, which agrees with the tutorial.
Recall that in Excel, the parameter of COS is in radians.
So "theta" (angle in degrees) is:
=DEGREES(ACOS(C1))
The result is 68.5624469663971, which rounds to 68.6 degrees.