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For a function $\sin[2x]$, the operand is $2x$. If we want know the value of the operand by hand, the function is simply $\arcsin(\sin[2x])=2x$. How to do this with Mathematica?

Here's what I tried:

ArcSin[Sin[2 x]]

Which, if you try it, does not provide any information.

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    $\begingroup$ Do you need to apply ArcSin, or could you just try First@Sin[2 x]; the latter will return the argument of Sin mechanically (for lack of a better word), rather than through calculation. $\endgroup$ – MarcoB Dec 13 '19 at 19:19
  • $\begingroup$ @MarcoB I get the error Syntax::sntxf: "First@" cannot be followed by "[Sin[2*x]]". $\endgroup$ – axsvl77 Dec 13 '19 at 19:21
  • $\begingroup$ I just want the 2x back. I think Mathematica has an easy way that I don't know. $\endgroup$ – axsvl77 Dec 13 '19 at 19:22
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    $\begingroup$ # & @@ Sin[2 x]? $\endgroup$ – kglr Dec 13 '19 at 19:27
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    $\begingroup$ This mechanism is pretty fiddly, though, because whatever you pass to First might be evaluated to a different form before First starts extraction of the first argument. For instance, First@Sin[1] works while First@Sin[0] doesn't. $\endgroup$ – kirma Dec 13 '19 at 19:30
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Perhaps what you are looking for is:

# & @@ Sin[2 x]

2 x

When the argument is a list and some elements of it have a numerical value we need to use Unevaluated to prevent evaluation of Sin:

# & @@ Unevaluated @ Sin[{2 x, π, 3., y}]

{2 x, π, 3., y}

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