Originally Posted by

**redsoxfan325** As I was messing around in Maple (yes I'm a nerd), I noticed something.

It appears as if the infinite chain $\displaystyle \sin(\cos(\sin(\cos(\sin(\cos(.....(\sin(\cos(x))) ))))))$ converges for all x.

It appears to be converging to a number very close to $\displaystyle \ln(2)$, but I don't think it actually does, unless it's really, really slowly.

The number (calculated for 7 sine-cosine pairs) is approximately $\displaystyle 0.69481969$.

Also, if you let the first term be cosine instead of sine, this chain gets close to $\displaystyle 0.768169156736795977462$.

Does anyone know anything about this?