In

Trigonometry Nest, the functions sin(cos(x)) and cos(sin(x)) were introduced, and it was proven that one of these functions is always greater than the other.

Taking this concept to infinity, which of these functions is greater: C(x)=cos(sin(cos(......(sin(x))))...))), or S(x)=sin(cos(sin(......(cos(x))))...)))?

How does the ratio C(x)/S(x) depend on x?

As long as nobody was commenting, I thought I'd try it in excel, just to see whether it really converged.

In fact, it seems to converge pretty quickly.

I have C(x) approximates .768169 for all x

S(x) approximates .694820 for all x

C(x) is greater