explain the difference between 1/(sinx) and ((sin^-1)x)

Question

anonymous · Answer

$$\frac{1}{sin(x)}=csc(x)$$
$$sin^{-1}(x)=arcsin(x)$$

anonymous · Answer

$1/\sin x$ is the inverse value of $\sin x$. $\sin^{-1} x$ is the inverse function of sine (of $x$).

anonymous · Answer

Sin(pi/6)=1/2
ArcSin(1/2)=pi/6

anonymous · Answer

Personally, I would always say arcsin if that's what I meant, the other can cause confusion.

anonymous · Answer

Writing $\sin^{-1}$ is actually very systematic since it follows the general composite function notation. $\sin^{-1}$ is an equivalent marking to that of $f^{-1}$, denoting the inverse function. "Going back one step." $\sin$ just happens to be a familiar function with a name we all recognise. The notation $\sin^{2}x$ again is misleading since it doesn't mean $\sin(\sin(x)))$ but $(\sin x)^2$.

anonymous · Answer

I look at it precisely in the reverse way, though (so do programmers).