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## Main Question or Discussion Point

I find this statement confusing from Wikipedia:

[tex]sin(y)=x\Leftrightarrow y=arcsin(x)+2k\pi\ \forall\ k\in\mathbb Z[/tex]

Is this statement false? "arcsin(x)" gives the principal value:[[itex]\frac{-\pi}{2},\frac{\pi}{2}[/itex]]. Therefore,specifically, "arcsin(x)" gives [itex]\frac{\pi}{3}\text{ but not}\frac{2\pi}{3}[/itex].

My textbook:

[tex]sin(y)=x\Leftrightarrow y=(-1)^{k}arcsin(x)+k\pi\ \forall\ k\in\mathbb Z[/tex]

I think my textbook's statement is more "complete".Or are the 2 statements both true?

[tex]sin(y)=x\Leftrightarrow y=arcsin(x)+2k\pi\ \forall\ k\in\mathbb Z[/tex]

Is this statement false? "arcsin(x)" gives the principal value:[[itex]\frac{-\pi}{2},\frac{\pi}{2}[/itex]]. Therefore,specifically, "arcsin(x)" gives [itex]\frac{\pi}{3}\text{ but not}\frac{2\pi}{3}[/itex].

My textbook:

[tex]sin(y)=x\Leftrightarrow y=(-1)^{k}arcsin(x)+k\pi\ \forall\ k\in\mathbb Z[/tex]

I think my textbook's statement is more "complete".Or are the 2 statements both true?