Question

To what number does \[\cos(\cos(\cos(\cos(\cos(\cos(\cos(\cos(...\cos(a)))))))))\]converge, where a is a real?

Answer 1

assuming it converges gimmick is to write
\[\cos(x) = x\] and solve

Answer 2

lol

Answer 3

that works

Answer 4

hey it doesn't :(

Answer 5

no w8 it does :-D

Answer 6

0.73908513321517

Answer 7

but does it converge? I think it does, although it's interesting to ask why.