# How to find the operand of a sinusoid?

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.

• 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. – MarcoB Dec 13 '19 at 19:19
• @MarcoB I get the error Syntax::sntxf: "First@" cannot be followed by "[Sin[2*x]]". – axsvl77 Dec 13 '19 at 19:21
• I just want the 2x back. I think Mathematica has an easy way that I don't know. – axsvl77 Dec 13 '19 at 19:22
• # & @@ Sin[2 x]? – kglr Dec 13 '19 at 19:27
• 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. – kirma Dec 13 '19 at 19:30

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}