Copy and paste the formulas below for x(t) and y(t) into the input boxes of the action figure to give a variety of interesting examples. Hit the enter key with the curser in one of the input boxes to tell the figure to read your new formulas.

x(t)	y(t)	Comments
cos[a*t]	sin[b*t]	Try varying a and b. Set tmax=6.28. Lissajous Figures
a*(t^2-1)	a*t*(t^2-3)/3	Tschirnhausen's cubic. Set tmin=-10 and tmax=10
cos[t]*sin[a*t]	sin[t]*sin[a*t]	Try varying a. Set tmax=6.28.
(1+1/a)*cos[t]+b*cos[(a-1)*t]/a	(1+1/a)*sin[t]-b*sin[(a-1)*t]/a	Try a=3 and b=1.1. Try a=4 and b=0.6. Set tmax=6.28.
3*a*t/(1+t^3)	3*a*t^2/(1+t^3)	Try tmin = -n, tmax = n with n = 5, 10, 20 Folium of Descartes
cos[t]*c*d/(1+c*cos[t])-d	sin[t]*c*d/(1+c*cos[t])	c is the eccentricity. The y-axis is the directrix and a focus is at -d. Set tmax=6.28.
a*tan[t]	a*(cos[t])^2	Witch of Agnesi
cos[t]*(2*a*cos[t]+b)	sin[t]*(2*a*cos[t]+b)	Limacon of Pascal tmin=-3.14 tmax=3.14
a*cos[t]*(1+b*cos[t])	a*sin[t]*(1+b*cos[t])	Cardioid. Set tmax=6.28, tmin=0
a*cos[t]/(1+(sin[t])^2)	a*sin[t]*cos[t]/(1+(sin[t])^2)	Leminscate of Bernoulli tmin=-3.14, tmax=3.14
a*cos[t]	a*sin[t]*cos[t]	Another figure eight tmin=-3.14, tmax=3.14
a*cos[t]	b*cot[t]	Bullet Nose tmin=-3.14, tmax=3.14
a/cos[t]	b/sin[t]	The cross curve tmin=-3.14, tmax=3.14
a*cos[t]*(1+cos[t])-a/2	a*sin[t]*(1-cos[t])	Deltoid tmin=-3.14, tmax=3.14
b+a*cos[t]	tan[t]*(b+a*cos[t])	Conchoid of Nicomedes tmin=-1.57, tmax=4.71
a*cos[t]*cot[t]	a*cos[t]	Kappa Curve tmax=6.28
a*sec[t]	a*sec[t]*tan[t]	Kampyle of Eudoxus tmin=-1.57, tmax=4.71 x4=a2(x2+y2)