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I'm trying to plot two parametric graphs as follows:

   alpha3[t_] := {Sin[2t]Cos[t],Sin[2t]Sin[t]}
   evoluta[t_] := alpha3[t]+(1/kappa[alpha3][t]) normal[alpha3][t]
   graph1 = ParametricPlot[alpha3[t]//Evaluate,{t,-2Pi,2Pi},PlotStyle->{{PlotRange -> 1}}]
   graph2 = ParametricPlot[evoluta[t]//Evaluate,{t,-2Pi,2Pi},PlotStyle->{{RGBColor[0.8,0.2,0.2],PlotRange ->1}}]
   Show[graph1,graph2]

The result obtained is:

enter image description here

I would like that the whole plot appears on the screen, however, PlotRange->All is not working for me?

How can I do so?

Extra (code for drawing evolute)

tangent[alpha_][t_]:=D[alpha[u],u]/Simplify[Factor[D[alpha[u],u].D[alpha[u],u]]]^(1/2) /. u->t
J:={{0,-1},{1,0}}
normal[alpha_][t_]:=J.tangent[alpha][t]
kappa[alpha_][t_]:=Det[{D[alpha[u],u],D[alpha[u],{u,2}]}]/
Simplify[D[alpha[u],u].D[alpha[u],u]]^(3/2)/.u->t
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  • $\begingroup$ Try ParametricPlot[{alpha3[t], evoluta[t]} // Evaluate, {t, -2 Pi, 2 Pi}, PlotRange -> All, PlotStyle -> {{}, Directive[RGBColor[0.8, 0.2, 0.2], Thick]}]. $\endgroup$ Mar 30, 2018 at 0:32
  • $\begingroup$ ok, even ParametricPlot[ {alpha3[t],evoluta[t]}//Evaluate,{t,-2 Pi,2 Pi}] works apparently $\endgroup$ Mar 30, 2018 at 0:36
  • $\begingroup$ Yes; I added PlotStyle just to show how to change styles for a specific curve. Remember to use Directive[] if you want to apply more than one style (e.g. color and thickness at the same time). $\endgroup$ Mar 30, 2018 at 0:38
  • $\begingroup$ You did not include the definitions of kappa or normal. Questions should include executable code. $\endgroup$
    – Bob Hanlon
    Mar 30, 2018 at 1:34
  • $\begingroup$ @BobHanlon I added the missing details, thanks $\endgroup$ Mar 30, 2018 at 10:09

1 Answer 1

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Since the OP has forgotten to include the sundry definitions, let me instead present a compact way to render a curve and its evolute:

f[t_] := {Sin[2 t] Cos[t], Sin[2 t] Sin[t]};

{{kappa[t_]}, {tangent[t_], normal[t_]}} = FrenetSerretSystem[f[t], t];

ParametricPlot[{f[t], f[t] + normal[t]/kappa[t]}, {t, 0, 2 π}]

quadrifolium and its evolute

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