Question

Is it possible to adjust manipulate option, so that this formula is written in a standard form: 5 Cos(2x + 1.85982), I mean that inside parentheses it is firstly written x, and then phase.

Also is there a way that this phase is written in terms of Pi, because I think it’s more meaningful for students to see phase in familiar form Pi/2 than 1.5708.

Thank you for any suggestions and answers.

Here is the code that I used:

Manipulate[
     Plot[A Cos[\[Omega] t + \[Phi]], {t, -4 Pi, 4 Pi}, AspectRatio -> 1, PlotRange -> 10], 
     Dynamic[A Cos[\[Omega] x + \[Phi]]], {{A, 5}, 1, 10, 1, Appearance -> "Labeled"}, 
     {\[Omega], 1, 5, 1, Appearance -> "Labeled"}, 
     {\[Phi], 0, 2 Pi, Appearance -> "Labeled"}]

Answer 1

Maybe you could do something like

Manipulate[
 Plot[A Cos[\[Omega] t + \[Phi]], {t, -4 Pi, 4 Pi}, AspectRatio -> 1, PlotRange -> 10], 
 Pane[Dynamic[A Cos[Row[{\[Omega] x, "+", \[Phi]}]]], {100, 30}],
 {{A, 5}, 1, 10, 1, Appearance -> "Labeled"},
 {\[Omega], 1, 5, 1, Appearance -> "Labeled"}, 
 {\[Phi], 0, 2 Pi, Pi/10, Appearance -> "Labeled"}]

Screenshot: