# Equivalent parametric plots don't look the same

ParametricPlot[ {1, Tan[t]}, {t, -Pi/3, Pi/3}]
ParametricPlot[ Sec[t] {Cos[t], Sin[t]}, {t, -Pi/3, Pi/3}]


The second parametrization does not plot like the first, how to make it plot without changing its form?

• use Evaluate in the second line:, i.e, ParametricPlot[Evaluate[Sec[t] {Cos[t], Sin[t]}], {t, -Pi/3, Pi/3}]. Or Evaluated->True, i.e., ParametricPlot[Sec[t] {Cos[t], Sin[t]}, {t, -Pi/3, Pi/3}, Evaluated -> True] – kglr Feb 27 '15 at 4:55
• Or include PlotRange -> {{-.1, 2.1}, {-1.9, 1.9}} – Bob Hanlon Feb 27 '15 at 4:59
• Thanks. Expected the plot defaults would automatically handle simple cases. – Narasimham Feb 27 '15 at 5:25

 ParametricPlot[Sec[t] {Cos[t], Sin[t]}, {t, -Pi/3, Pi/3},

• @Narasimham. The heuristics Mathematica uses for choosing plot range when none is specified are unknown to me. But giving the option PlotRange to manually override the automatic choice will always solve the kind of problem you have encountered. – m_goldberg Feb 27 '15 at 6:19