This is a "What-If-Not" variation on the iteration theme. Instead of using numbers, we are using trig functions in the spirit is Chebyshev Polynomials [url]http://en.wikipedia.org/wiki/Chebyshev_polynomials[/url] to iterate the rule [math]f_{n+2}(x)=\frac{f_{n+1}(x) + k}{f_{n}(x)}[/math]. You can change the two starting functions, as well as the number you are adding in the numerator.