animate a parametric plot

define the components and set the t-interval

Clear[x,y,t,tmin,tmax]
x[t_] := 5Cos[3t]
y[t_] := 5Sin[3t]
tmin = 0; tmax = 2 Pi/3;

a static plot can aid in setting a common graphing window for the animation

ParametricPlot[{x[t],y[t]},{t,tmin, tmax}]

give good values for the x’s and y’s in the graphing window. 
then play the animation.  watch the head of the vector trace out the curve. 
increase the denominator for delta t to see a smoother animation.

Clear[xmin,xmax,ymin,ymax,deltat]

xmin = -6; xmax = 6; ymin = -6; ymax = 6;

deltat=(tmax-tmin)/20.;Manipulate[Show[{ParametricPlot[{x[t],y[t]},{t,tmin,a},PlotRange->{{xmin,xmax},{ymin,ymax}}],
Graphics[{Red,Arrow[ {{0,0}, {x[a],y[a]} }]}]  }],
{a,tmin+deltat,tmax,deltat}]