Helix Curve along the z-axis

Problem #11.5.37

x[t_]:=.5*Cos[15*t]; y[t_]:=(8+Sin[15*t])*Cos[t];z[t_]:=(8+Sin[15*t])*Sin[t];

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

ParametricPlot3D[{x[t],y[t],z[t]},{t,0,2Pi},ColorFunction->Function[{x,y,z},Hue[.65*(1-z)]], AxesLabel->{"x","y","z"},PlotLabel->"Problem 11.5.37", PlotStyle->{Thick},BoxRatios->Automatic]

Problem #11.5.38

x[t_]:=2*Cos[t]; y[t_]:=4*Sin[t];z[t_]:=Cos[10*t];

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

ParametricPlot3D[{x[t],y[t],z[t]},{t,0,2Pi},ColorFunction->Function[{x,y,z},Hue[.65*(1-z)]], AxesLabel->{"x","y","z"},PlotLabel->"Problem 11.5.38", PlotStyle->{Thick},BoxRatios->Automatic]

Problem #11.5.40

x[t_]:=Cos[t]*Sin[3*t]; y[t_]:=Sin[t]*Sin[3*t];z[t_]:=Sqrt[t];

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

ParametricPlot3D[{x[t],y[t],z[t]},{t,0,9},ColorFunction->Function[{x,y,z},Hue[.65*(1-z)]], AxesLabel->{"x","y","z"},PlotLabel->"Problem 11.5.40", PlotStyle->{Thick},BoxRatios->Automatic]