solution=NDSolve[{y''[t]==-Sin[y[t]],y[0]==Pi/6.0,y'[0]==0.},y,{t,0,1000}]

Plot[Evaluate[y[t]/.solution],{t,0,100}]

Plot[{Evaluate[{Sin[y[t]],-1.0*Cos[y[t]]}/.solution]},{t,0,100}]

ParametricPlot[{Evaluate[{Sin[y[t]],-1.0*Cos[y[t]]}/.solution]},{t,0,100},PlotRange->{{-1,1},{-1,0}}]

Graphics[{{PointSize[.025],{Red,Point[{Sin[y[0]],-1.0*Cos[y[0]]}]}}/.solution},PlotRange->{{-1,1},{-1,0}},Axes->True,Ticks->False,ImageSize->500]

Animate[Graphics[{{PointSize[.025],{Red,Point[{Sin[y[t]],-1.0*Cos[y[t]]}]},Line[{{0,0},{Sin[y[t]],-1.0*Cos[y[t]]}}]}/.solution},PlotRange->{{-1,1},{-1.2,0}},Axes->True,Ticks->False,ImageSize->500],{t,0,100,0.1},AnimationRate->1.,SaveDefinitions->True]