10-1 Parametric Equations.sagews

t = var('t')
parametric_plot((t^2, t^3), (t, -1, 2))

animate([parametric_plot((t^2, t^3), (t, -1, c)) for c in srange(-0.9, 2.01, 0.1)], xmin=0, xmax=4, ymin=-1, ymax=8)

parametric_plot((sin(10*t), cos(13*t)), (t, 0, 2*pi))

parametric_plot((sin(t + cos(100*t)), cos(t + sin(100*t))), (t, 0, 2*pi))

parametric_plot((1*sin(t) + 2*sin(4*t) + 3*sin(7*t) + 2*sin(10*t), 1*cos(t) + 2*cos(4*t) + 3*cos(7*t) + 2*cos(10*t)), (t, 0, 2*pi))

parametric_plot(((cos(5*t)+2)*cos(t), (cos(5*t)+2)*sin(t)), (t, 0, 2*pi))

u, v = var('u,v')
fx = (3+sin(v)+cos(u))*cos(2*v)
fy = (3+sin(v)+cos(u))*sin(2*v)
fz = sin(u)+2*cos(v)
parametric_plot3d([fx, fy, fz], (u, 0, 2*pi), (v, 0, 2*pi), mesh=True, color="red")