The trefoil knot
x = (2 + Cos[1.5 t]) Cos[t]; y = (2 + Cos[1.5 t]) Sin[t]; z = Sin[1.5t]; ParametricPlot3D[{x,y,z},{t,0,10}]
Notice that we have specified parameter values 0 < t < 10. We can specify a longer interval of parameter t values:
ParametricPlot3D[ {x,y,z},{t,0,12.5}]
x = Cos[t]; y = Sin[t]; z = 2-Sin[t]; ParametricPlot3D[ {x,y,z},{t,0,6}]
x = t; y = t^2; z = t^3; ParametricPlot3D[ {x,y,z,RGBColor[1,0,0]}, {t,-2,2} ]
x = (4+Sin[20t])Cos[t]; y = (4+Sin[20t])Sin[t]; z = Cos[20t]; ParametricPlot3D[ {x,y,z}, {t, 0, 2 Pi} ]
This picture is not good, notice the sharp corners which the true curve does not have. We need to increase the number of points used by default in the plot:
ParametricPlot3D[ {x,y,z},{t,0,2 Pi},PlotPoints->300]
You can use the program