Manipulate[ ParametricPlot[ does not produce graphs for defined functions

Questions
,
1

I have a weird problem to which I cannot figure out the answer. When defining two functions and then using them inside ParametricPlot in a Manipulate, no graph is produced. Pasting the functions directly into ParametricPlot creates the Plot. I tried to use Evaluate, but no success. What am I not getting? Attached is a notebook that shows what works and what does not.

Thanks for any explanation as to what isgoing on.

x[t_] := R Cos[t] + r Cos[k t]
y[t_] := R Sin[t] + r Sin[k t]

Manipulate[
 ParametricPlot[{x[t], y[t]}, {t, 0, 2 \[Pi]}, Axes -> True, 
  PlotRange -> {{-4, 4}, {-4, 4}}, 
  PlotStyle -> {Thick, Red}], {{R, 1}, 1, 2}, {{r, .5}, -1, 
  2}, {{k, 7}, 1, 11}]

(* this one did not work*)

Manipulate[
 ParametricPlot[{R Cos[t] + r Cos[k t], R Sin[t] + r Sin[k t]}, {t, 0,
    2 \[Pi]}, Axes -> False, PlotRange -> {{-4, 4}, {-4, 4}}, 
  PlotStyle -> {Thick, Red}], {{R, 1}, 1, 2}, {{r, .5}, -1, 
  2}, {{k, 7}, 1, 11}]

(* This one work s perfectly *)

xx[t_] = R Cos[t] + r Cos[k t];
yy[t_] = R Sin[t] + r Sin[k t];

Manipulate[
 ParametricPlot[{xx[t], yy[t]}, {t, 0, 2 \[Pi]}, Axes -> True, 
  PlotRange -> {{-4, 4}, {-4, 4}}, 
  PlotStyle -> {Thick, Red}], {{R, 1}, 1, 2}, {{r, .5}, -1, 
  2}, {{k, 7}, 1, 11}]

(*Tried with = instead of := function assignment, but that did not change anything *)
2

Dear Silvia,

please do try this:

x[t_] := R Cos[t] + r Cos[k t]
y[t_] := R Sin[t] + r Sin[k t]

Manipulate[
 ParametricPlot[{x[t], y[t]} /. {R -> RR, r -> rr, k -> kk}, {t, 0, 
   2 \[Pi]}, Axes -> True, PlotRange -> {{-4, 4}, {-4, 4}}, 
  PlotStyle -> {Thick, Red}], {{RR, 1}, 1, 2}, {{rr, .5}, -1, 
  2}, {{kk, 7}, 1, 11}]

Cheers,
M.