Does this work for you:
PolarPlot[{ArcCos[t], -ArcCos[t]}, {t, -1,1}]
Update: (Sjoerd C. de Vries comment)
For all r
r=(+/-)ArcCos[t]+2 n Pi
Taking few of r results:
Show[Table[
PolarPlot[{ArcCos[t], -ArcCos[t]} + n 2 Pi, {t, -1, 1},
PlotRange -> All], {n, -10, 10}]]