(*A simple graph in parametric*)

ParametricPlot[{Cos[θ],Sin[θ]},{θ,π,4π}]

(*Manipulating the radius and fixing the viewing window*)

Manipulate[
ParametricPlot[{r*Cos[θ],r*Sin[θ]},{θ,π,4π},PlotRange->{{-2.5,2.5},{-2.5,2.5}}],
{{r,1},0.5,2}]

(*Adding a second manipulate to rotate the graph. We've also thickened the graph and changed it to purple*)

Manipulate[
ParametricPlot[{r*Cos[θ+s],r*Sin[θ+s]},{θ,π,2π},PlotStyle->{Purple,Thick},PlotRange->{{-2.5,2.5},{-2.5,2.5}}],
{{r,1},0.5,2},{{s,0},0,2π}]

(*Allowing only a discrete range of radii for the circle*)

Manipulate[
ParametricPlot[{r*Cos[θ+s],r*Sin[θ+s]},{θ,π,2π},PlotStyle->{Purple,Thick},PlotRange->{{-2.5,2.5},{-2.5,2.5}}],
{{r,1},{0.5,1,2}},{{s,0},0,2π}]

(*Watching the graph be drawn*)

Manipulate[
ParametricPlot[{r*Cos[θ],r*Sin[θ]},{θ,π,t},PlotRange->{{-2.5,2.5},{-2.5,2.5}}],
{{r,1},0.5,2},{{t,π+0.0001},π+0.0001,3π}]