What is this expression means? $\sin^{-2}x$ I know this is very silly question but I didn't know how to research it in google. Please bare with me on this one. I have two thoughts:

$$\sin^{-2}x = \frac{1}{\sin^2x}$$

I think this cannot be possible. Or is it:

$$\sin^{-2}x = \arcsin^2x$$

I didn't make up this question, I mean kinda. I am developing an android application which solves mathematical equations for demonstration purposes. I was brainstorming what the user can input, I came up with this expression.
 A: For a computer application, I would suggest you avoid all ambiguity by forcing the user to type
$$
(\sin x)^2
$$
for $\sin^2(x)$, and
$$
\arcsin x
$$
for the inverse function. Don't allow $\sin^n (x)$ as it is abusive shorthand which has done more to confuse people than help.
However, it's also worth noting that Wolfram Alpha interprets $\sin^{-2}(x) = \frac{1}{(\sin x)^2}$, whereas $\sin^{-1}(x) = \arcsin x$. More generally, it appears that $n = 1$ is a special case in $\sin^n(x)$ and otherwise it is interpreted as $(\sin x)^n$.

The reason $\sin^n(x)$ is bad notation for $(\sin x)^n$ is that in most contexts, $f^n(x)$ means the $n$th iterate of $f$.
In particular, the $-1$th iterate of an invertible function is the inverse,
so $\sin^{-1}$ would actually be a natural way to denote $\arcsin$.
On the other hand, the problem with $\sin^{-1}(x)$ for $\arcsin$ is of course that it conflicts with the hugely widespread notation $\sin^2(x)$.
You really can't win.
A: (1) If you found this in a book, paper, or web page, without an explanation, that is a bad book, paper or web page.
(2)  Do not use this notation yourself.
