cos(-56)= 0.559192903471
cos(cos(-56))= 0.999952373947
cos(cos(cos(-56)))= 0.999847709663
cos(cos(cos(cos(-56))))= 0.999847741541
cos(cos(cos(cos(cos(-56)))))= 0.999847741531
cos(cos(cos(cos(cos(cos(-56))))))= 0.999847741531
cos(cos(cos(cos(cos(cos(cos(-56)))))))= 0.999847741531
As you can see, it begins to repeat. This happens with cos(n), and cos(cos(n)), and so on.
What, mathematically, is the cause for this?