cfbb=Function[{x,y,t,r},ColorData["BrightBands"][r]];
cfdb=Function[{x,y,t,r},ColorData["DarkBands"][r]];
pp1=PolarPlot[Exp[Cos[t]^2+Sin[t]]-3Cos[4t]+Sin[t/12],
{t, 0,6\[Pi]},ColorFunction->cfbb];
pp2=PolarPlot[-Floor[t]*Sin[t]/2,{t,0,6Pi},
ExclusionsStyle->Dashed,ColorFunction->cfdb];
Show[pp1,pp2,Axes->False,PlotStyle->Thick,ImageSize->500]
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