Uniform Circular motion

x[t_]:=Cos[t]
y[t_]:=Sin[t]
slope[t_]=y'[t]/x'[t]
tangentLine[xx_,t_]:=y[t]+slope[t](xx-x[t])
ParametricPlot[{x[t],y[t]},{t,0,2Pi}]

plot=ParametricPlot[{x[t],y[t]},{t,0,2Pi}];
Manipulate[
Show[
plot,
ListPlot[{{x[time],y[time]}},PlotMarkers->{ }],
Plot[tangentLine[xx,time],{xx,-2,2}]
],
{time,0.001,2Pi,.1}
]