The convention that $\sin^2 x = (\sin x)^2$, while in general $f^2(x) = f(f(x))$, is often called illogical, but it does not lead to conflicts because nobody uses $\sin(\sin x)$.


But is this really true? Or is there a real-world application in which $\sin(\sin x)$ occurs? Or maybe something a bit more general, like $\sin(C \sin x)$ for some constant $C \neq 0$?



Is there any use for $\sin(\sin x)$?
The intensity of light diffracted at a slit as a function of the angle actually involves a term $\sin\left(\frac{\alpha\beta}{2}\sin(\theta)\right)$, see


<https://en.wikipedia.org/wiki/Fraunhofer_diffraction>


(I'm no physicist at all, but this has been stuck in my head since high school just because it is such an unusual term to encounter naturally)


