Possible Duplicate:
$\arcsin$ written as $\sin^{-1}(x)$
I have worked a bit on trigonometry today, and something strikes me as inconsistent.
In the book, the notation for the inverse sine function is $\sin^{-1}$, but the same notation is also used in $\sin^2$ meaning $(\sin x)^2$.
Are there any alternate notations which avoid this ambiguity?
Some examples:
$\sin30^\circ = 0.5$
$\sin^2 30^\circ = (\sin 30^\circ)^2 = 0.25$
However, inverse sine does not work that way:
$\sin^{-1} 30^\circ \ne (\sin 30^\circ)^{-1}$
$\sin^{-1} 30^\circ = $ Error or complex number?
$(\sin 30^\circ)^{-1} = 2$
The potential confusion only gets worse if you use radians, as they are in the range [-1, 1] for [-57°, 57°].:
$\sin^{-1} 0.524 = 0.551$
$(\sin 0.524)^{-1} = 2$
And what if you want both at the same time? You are forced to use parentheses, thus breaking any consistency: $(\sin^{-1} x)^2$