Since sin⁻¹(x) means the inverse of sin(x), also written as arcsin(x), how would you write 1/sin(x)? Since sin²(x) actually does mean sin(x) * sin(x), can you write 1/(sinx *sinx) as sin⁻²(x)?
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1You can write $1/\sin x$ as $\text{cosec},x$. – Angina Seng Apr 19 '19 at 16:19
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1It is $$\csc(x)=\frac{1}{\sin(x)}$$ – Dr. Sonnhard Graubner Apr 19 '19 at 16:21
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1And it is $$\frac{1}{\sin(x)\sin(x)}=\frac{1}{\sin^2(x)}=\sin^{-2}(x)$$ – Dr. Sonnhard Graubner Apr 19 '19 at 16:23
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1Normally I use $\arcsin(x)$ for inverse functions, I prefer this notation – Kandinskij Apr 19 '19 at 16:23
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This is why $\sin^{-1}{(x)}$ is disliked by many mathematicians for its use to describe $\arcsin{(x)}$. – Peter Foreman Apr 19 '19 at 16:23
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@PeterForeman I like $\sin^{-1}x$. I don't like $\sin^2 x$, since that should be $\sin(\sin x)$. – Angina Seng Apr 19 '19 at 16:27
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@Dr.SonnhardGraubner Do you really use $\sin^{-2}x$ in your writings? – Angina Seng Apr 19 '19 at 16:27
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@LordSharktheUnknown Do you think that $\sin^{-2}{(x)}$ should mean $\arcsin{(\arcsin{(x)})}$? – Peter Foreman Apr 19 '19 at 16:28
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@PeterForeman That makes sense! Do you agree with Dr.S.G. about what it should be? – Angina Seng Apr 19 '19 at 16:29
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I believe the only ambiguity is when it comes to what $\sin^{-1}{(x)}$ means. I believe that the notation $\sin^n{(x)}$ should be used to represent $(\sin{(x)})^n$, but that is just my (and Wolfram: Alphas) opinion. – Peter Foreman Apr 19 '19 at 16:31