How do I implement a condition on a plot in a Manipulate expression?

Question

I want to implement a condition to affects the behavior of a plot made in a Manipulate expression.

Suppose I have

Manipulate[Plot[Sin[nx],{x, 0, 5}],{n, 0, 6, 1}]

I want to change it so that for n odd, I get

 Manipulate[Plot[Sin[nx], {x, 0, 5}],{n, 0, 6, 1}]

and for n even I get

 Manipulate[Plot[Cos[nx], {x, 0, 5}], {n, 0, 6, 1}]`

But I want it in the same plot in the same Manipulate with n integer

How can I do this?

Answer 1

You can do it by defining a new function

sincos[x_, n_?OddQ] := Sin[n x]
sincos[x_, n_?EvenQ] := Cos[n x]

which expresses your conditions. Then

Manipulate[
  Plot[sincos[x, n], {x, 0, 2. π}],
  {n, 0, 6, 1, AppearanceElements -> All}]

Answer 2

Another possibility is to use Which

Manipulate[
 Module[{f, x, title},

  Which[
   EvenQ[n], f = Cos[n x]; title = "cos(" <> ToString@n <> " x)",
   True, f = Sin[n x]; title = "sin(" <> ToString@n <> " x)"
   ];
  Plot[f, {x, -Pi, Pi},
   Frame -> True,
   FrameLabel -> {{"f(x)", None}, {"x", title}},
   GridLines -> Automatic, GridLinesStyle -> LightGray,
   PlotStyle -> Red,
   BaseStyle -> 14]
  ],
 {{n, 1, "n?"}, 0, 10, 1, Appearance -> "Labeled"}
 ]