I noticed something odd while messing around on my calculator.
$\lim_{n\to \infty} \cos^n(c)=0.7390851332$ Where $c$ is a real constant.
With $\cos^n(c) =\underbrace{\cos \circ\cos \circ\cos \circ \cdots \circ \cos \circ \cos}_{n \text{ times}}(c)$
My calculator is in radians and I got this number by simply taking the cosine of many numbers over and over again. No matter what number I use I always end up with that number. Why does this happen and where does this number come from?