Helix Curve along the z-axis

Define parametric curve coordinate functions

x[t_]:=Sin[2*Pi*t]; y[t_]:=Cos[2*Pi*t];z[t_]:=t;

Use the “ParametricPlot3D” command to graph the curve in 3-D space.

ParametricPlot3D[{x[t],y[t],z[t]},{t,0,2},ColorFunction->Function[{x,y,z},Hue[.65*(1-z)]], AxesLabel->{"x","y","z"},PlotLabel->"Parametric Plot of Circular Helix", PlotStyle->{Thick}, BoxRatios->{1,1,1}]

Modify the winding frequency by changing the trigonometric frequencies.

x[t_]:=Sin[10*Pi*t]; y[t_]:=Cos[10*Pi*t];z[t_]:=t;

ParametricPlot3D[{x[t],y[t],z[t]},{t,0,2},ColorFunction->Function[{x,y,z},Hue[.65*(1-z)]], AxesLabel->{"x","y","z"},PlotLabel->"Parametric Plot of Circular Helix", PlotStyle->{Thick}, BoxRatios->{1,1,1}]