Infinitely Concatenated Sine and Cosine Using a graphing calculator, if one concatenates sine and cosine repeatedly, i.e.
$$y=\sin(\cos(\sin(\cos(x))))$$
the graph appears to approach a horizontal line, suggesting that at infinite concatenation, there is a single value of the function for all $x$.  Is this correct?  If so is this value known?

Taking infinite concatenation into account,and writing $y$ as $$y=\sin(\cos(y))$$
Wolfram Alpha gives the solution to be a constant namely $$0.694819690731$$
