Plotting Parametric Curves in Mathematica

Math 104 Calculus II, April 5, 2019
T. Ratliff, Wheaton College
ratliff_thomas@wheatoncollege.edu

Plot r(t)=< cos(t), sin(t)>

Try different values for t to see what part of the curve is traced out

ParametricPlot[{Cos[t],Sin[t]},{t,0,Pi}]

ParametricPlot[{Cos[t],Sin[t]},{t,0,3Pi/2}]

Compare to r(t)=< cos(t), - sin(t) >

ParametricPlot[{Cos[t],-Sin[t]},{t,0,Pi}]

Plot r(t) = < cos(t), sin(t), t>

ParametricPlot3D[{Cos[t],Sin[t],t}, {t,0,4Pi}]

Plot r(t) = < cos(t), sin(t), cos(2t)>

ParametricPlot3D[{Cos[t],Sin[t],Cos[2t]}, {t,0,4Pi}]

Plotting Reading Questions r(t) = < sin(2t), t^2 >

ParametricPlot[{Sin[2t],t^2},{t,0,3}]

We can show two different Mathematica graphics objects at the same time using the Show[ ] command.
r(1) = < sin(2), 1> and
r’(1) = < 2 cos(2), 2>

p1=ParametricPlot[{Sin[2t],t^2},{t,0,3}];
p2=Graphics[{Red, Thickness[0.01],Arrow[ { {Sin[2],1}, { 2Cos[2]+Sin[2],3}}]}];
Show[p1,p2]