Why is arcsin represented with the ^(-1) notation?

Question

So in trigonometry, we have sin, secant (which is one over sin) and arcisn. Why is arcsin sometimes represented with sin^-1? sin^2 means sin to the second power, but sin^-1 explicitly does not mean sin to the negative first power, as that would be the secant, not the arcsin. Why this confusion in notation?

Answer 1

If we agree, that $f^{-1}$ means the inverse of $f$, we may obtain such strange notation. Let us observe, that $x^{-1}=1/x$ is not the inverse of $f(x)=x$, $x^{-3}$ is not the inverse of $x^3$ and so on.