I am not sure I understand what you mean by How can I draw where t is'. But if you want to drawParametricPlotint` the command is
x = Exp[1/2]*Cos[(Pi/4) t] + Cos[2 Pi*t] ;
y = Exp[1/3]*1/2 Sin[Pi*t] + Sin[2 Pi*t];
a = -1; b = 1;
ParametricPlot[{x, y}, {t, a, b}]
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