Question

I have a more general question, will 1/sin(x) ever be written as sin^(-1)(x)? Or any trig question for that matter. I had a problem with this in an assignment and it took a long time to figure out that they meant arcsin(x) so the notation is confusing me.

Answer 1

No, because:
\[\frac{ 1 }{ \sin(x) }\neq \sin^{-1} (x)\]

Answer 2

This is simply a matter of convention in how we use the notation.\[\sin ^2 x=(\sin x)^2\] and\[\sin ^5x=(\sin x)^5\]but\[\sin ^{-1}x \neq(\sin x)^{-1}\]because this notation is reserved for use as an alternative way of writing arcsin x.

Answer 3

Ok thank you, hopefully my mind won't jump to 1/sin(x) now when I see that lol.