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?

Since neither depends on the original x, either one could start out (that is, the innermost) with sin(x) or cos(x).  It follows that C(x) = cos(S(x)) and S(x) = sin(C(x)).

Posted by Charlie on 2005-11-07 10:49:43