Although I understand that $\sin^2x$ refers to $(\sin x)^2$, and not $\sin(\sin(x))$, I find this notation to be confusing—often it can hamper my thinking. For instance, if I was solving the following equation:
$$ \sin^2x-\frac{7}{2}\sin x-2=0 $$
I might not realise that there is a squared term and a linear term, and hence it is a quadratic in $\sin x$. If on the other hand I wrote:
$$ (\sin x)^2-\frac{7}{2}\sin x-2=0 $$
then it would be much clearer to me what is going on. So what is the best alternative to writing $\sin^2x$? The obvious answer is to write $(\sin x)^2$, but at times this can feel cluttered, particularly if there are other bracketed terms. So is there a better solution that avoids this notational issue?
One idea is to get goofy with $\sin(x)$, which you could denote $\sin_x$ which isn't confusing since sine isn't taking any arguments besides $x$ in that equation. You could terse-ify this even more to $\mathrm{s}_x$. So you get $$ \mathrm{s}_x^2-\frac{7}{2}\mathrm{s}_x-2=0 $$ But this is all just a complicated way to do basically what Nate did here and say "let $\mathrm{s}_x = \sin(x)$ ..."