Parametric CurvesNatacha Fontes-Merz, Kris Green, and Sarah RaynorSusie the rebellious clownfish is swimming away from the school one day. Sushi's position as a function of time is given by x(t)=(2sin(t)cos(2t),2sin(t)sin(2t),2cos(t))We are going to use Maple to understand her travels.restart:with(plots):Visualizing her PathOur first goal is to plot her path. We need to define x(t) for Maple:x:=t->2*sin(t)*cos(2*t);
y:=t->2*sin(t)*sin(2*t);
z:=t->2*cos(t);
starttime:=0;
endtime:=2*Pi;We are now set to plot her motion in the xy-plane:plot([x(t),y(t),t=starttime..endtime]);We can also animate the curve, which will allow us to see where she starts and which way she travels:animatecurve([x(t),y(t),t=starttime..endtime],numpoints=1000,frames=25);