How to simulate Placed in workaround for PlotLegends ParametricPlot bug?

Question

I'd like Legended output for call like:

rcap = {Cos[#], Sin[#]} & ;
p1 = ParametricPlot[{Sin[t] rcap[t], Sin[t]^2 rcap[t]}, {t, 0, Pi},
  PlotRange -> {-1, 1}, AxesLabel -> {x, y}
  , PlotLegends ->
   Placed[{"sin(\[Theta])",
     "\!\(\*SuperscriptBox[\(sin\), \(2\)]\)(\[Theta])"}, {Right,
     Bottom}]
  ]

But have hit the ParametricPlot has PlotLegends bug detailed in ParametricPlot and PlotLegends don't seem to cooperate .

I applied the list of functions answer to my plot (adding expressions for my labels) like so:

x1 = With[{funcList = {Sin[t] rcap[t], Sin[t]^2 rcap[t]},
   labelList = {"sin(\[Theta])",
     "\!\(\*SuperscriptBox[\(sin\), \(2\)]\)(\[Theta])"}
   }, With[{n = Length@funcList},
   Legended[
    ParametricPlot[funcList, {t, 0, Pi}, PlotRange -> {-1, 1},
     AxesLabel -> {x, y}],
    LineLegend[(ColorData[1][#]) & /@ #, labelList[[#]]] &@Range@n]]
  ]

which does successfully include a legend:

however, the placement of the legend text is outside of the image. Is there a way to add Placed like options to the Legended function?

Answer 1

From Legended >> Details:

x1 = With[{funcList = {Sin[t] rcap[t], Sin[t]^2 rcap[t]}, 
           labelList = {"sin(\[Theta])", "\!\(\*SuperscriptBox[\(sin\), \(2\)]\)(\[Theta])"}}, 
  With[{n = Length@funcList}, 
   Legended[ParametricPlot[funcList, {t, 0, Pi}, PlotRange -> {-1, 1}, AxesLabel -> {x, y}], 
       Placed[LineLegend[(ColorData[1][#]) & /@ #, labelList[[#]]] &@Range@n, {Right, Bottom}]]]]

You can also use PlotLegends instead of Legended as follows:

x1 = With[{funcList = {Sin[t] rcap[t], Sin[t]^2 rcap[t]}, 
   labelList = {"sin(\[Theta])", "\!\(\*SuperscriptBox[\(sin\), \(2\)]\)(\[Theta])"}}, 
  With[{n = Length@funcList}, 
   ParametricPlot[funcList, {t, 0, Pi}, PlotRange -> {-1, 1}, AxesLabel -> {x, y},
    PlotLegends -> Placed[LineLegend[ColorData[1][#] & /@ Range@n, labelList[[Range@n]]], 
                  {Right, Bottom}]]]]
 (* same picture *)