For this particular example a 2D slider works quite well:
Manipulate[
Plot[{Norm[p] Sin[2 \[Pi] t + ArcTan[p]],
Norm[p] Sin[2 \[Pi] t + ArcTan[p]]}, {t, 0, 1},
PlotRange -> {{0, 1}, {-3, 3}}],
{{p, {0, 0}}, {-2, -2}, {2, 2}}]
A variation:
Manipulate[
Row[{Plot[{Norm[p] Sin[2 \[Pi] t + ArcTan[p]],
Norm[p] Sin[2 \[Pi] t + ArcTan[p]]}, {t, 0, 1},
PlotRange -> {{0, 1}, {-3, 3}}],
Graphics[Locator[Dynamic@p], PlotRange -> 2, Frame -> True]}],
{{p, {0, 0}}, {-2, -2}, {2, 2}, ControlType -> None}]
