Sine of the times.

[Albert Chan]

I like sin(x)^2 notation. Say out loud, it is the same order: sine x squared.

Inverse Trig Notation: What Do sin^-1 and arcsin Mean?

Quote:you find that early forms of "arcsin" arose in the 1700s, and the sin^2 notation came at the same time;
sin^-1 was introduced in 1813.

This may explain why sin^2(x) cannot mean sin(sin(x)), I wish it did.
Notation were already taken long time ago.