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Possible Duplicate:
$\arcsin$ written as $\sin^{-1}(x)$

When I learnt the trig identity $\sin^2\theta + \cos^2\theta \equiv 1$, I learnt that $\sin^2\theta = (\sin\theta)^2$.

So why isn't $\sin^{-1}\theta = (\sin\theta)^{-1} = \dfrac{1}{\sin\theta}$?

Because $\csc\theta = \dfrac{1}{\sin\theta} $, but $\csc\theta \ne \sin^{-1}\theta$

How can these two same notations, just with different numbers, mean different things?

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    In the good old days, the notation $\arcsin x$ was the common one. The greater current popularity of $\sin^{-1} x$ is probably due to calculators: $\arcsin$ does no fit nicely into the cramped space above the $\sin$ buton.2012-06-22

5 Answers 5