Sign change of sine function

Question

I was trying to extract the parameter of the phase term of the sine function, and I found the problem that Mathamtica automatically try to change the sign of the sine function.

I got negative number or positive amplitude from the sine function. I don't really care what sine I am getting, but I want to get is consistent sign. Do I have a way to fix the sign of the amplitude or frequency part of the sine function?

example

2 Sin[2 x - 1]
2 Sin[-2 x - 1]
-2 Sin[-2 x - 1]
-2 Sin[2 x - 1]

Current output

-2 Sin[1 - 2 x]
-2 Sin[1 + 2 x]
2 Sin[1 + 2 x]
2 Sin[1 - 2 x]

Desired output

2 Sin[2 x - 1]
2 Sin[-2 x - 1]
2 Sin[1 + 2 x]
2 Sin[1 - 2 x]

Answer 1

This implementation ensures that Sin would not evaluate immediately.

ClearAll@times;
SetAttributes[times, HoldAllComplete];
times /: times[Times[x_, Sin[y_]]] /; Positive[x] := x HoldForm[Sin[y]];
times /: times[Times[x_, Sin[y_]]] := (-x) Sin[Times[-1, y]];

times[2 Sin[2 x - 1]]
times[2 Sin[-2 x - 1]]
times[-2 Sin[-2 x - 1]]
times[-2 Sin[2 x - 1]]

(*

2 \!\(\*TagBox[RowBox[{"Sin", "[",RowBox[{RowBox[{"2", " ", "x"}], "-", "1"}], "]"}],HoldForm]\)
2 \!\(\*TagBox[RowBox[{"Sin", "[",RowBox[{RowBox[{RowBox[{"-", "2"}], " ", "x"}], "-", "1"}], "]"}],HoldForm]\)
2 Sin[1 + 2 x]
2 Sin[1 - 2 x] *)

Answer 2

If you only want to print the Sin with the arguments unchanged you can use Defer or HoldForm:

Defer[Sin[2x + 1]]
HoldForm[Sin[2x + 1]]
(* Sin[2x + 1] *)
(* Sin[2x + 1] *)

Another possibility is to use Inactivate to inactivate either the whole expression or just the Plus symbol:

Of course, each of the above has a very specific usage and is more or less suitable depending on how you want to handle the expression afterwards.