Plot[Cos[t], {t, 0, 6 Pi}]

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 6 Pi}]

ParametricPlot[{Cos[t/2], Sin[t]}, {t, 0, 6 Pi}]

{x,y}

MatrixForm[{x,y}]

{{Cos[phi], -Sin[phi]}, {Sin[phi], Cos[phi]}}

MatrixForm[{{Cos[phi],-Sin[phi]},{Sin[phi],Cos[phi]}}]

{{Cos[phi], -Sin[phi]}, {Sin[phi], Cos[phi]}} . {x,y}

MatrixForm[{x Cos[phi]-y Sin[phi],y Cos[phi]+x Sin[phi]}]

rot[phi_] := {{Cos[phi], -Sin[phi]}, {Sin[phi], Cos[phi]}}

MatrixForm[rot[45 Degree]]

omegaPendulum = 1.0;
omegaEarth = 0.2;
xy[t_] := {Cos[omegaPendulum*t], 0};
xyRot[t_] := rot[omegaEarth*t] . xy[t];
ParametricPlot[xyRot[t], {t, 0, 10 Pi}]

(* If this shows a blank graph, you need to do 
 "Evaluation" -> "Evaluate Notebook" so that the
 plot can use the definition of xyRot, etc. *)
Animate[ParametricPlot[xyRot[t], {t, 0, tmax}], {tmax, 0, 10 Pi}]

(* This adds a small circle to the plot, showing (x,y) at tmax *)
Animate[
Show[
ParametricPlot[xyRot[t], {t, 0, tmax}],
Graphics[Circle[xyRot[tmax], 0.05]]
],
{tmax, 0, 40 Pi},
AnimationRate->0.03
]