4206.sagews

var('t')
parametric_plot( (cos(t), sin(t)), (t, 0, 3*pi/2), axes_labels=('x', 'y'))

var('t')
r=(cos(t), sin(t))
tbounds=(0, 2*pi)
tmin,tmax=tbounds
@interact
def myplot(tt=slider(tmin.n(), tmax.n(),default=((tmin+tmax)/2).n())):
    p=parametric_plot(r, (t, tmin, tmax),alpha=0.5)
    background=parametric_plot(r, (t, tmin, tt),thickness=3)
    show(p+background)

var('t')
r=(cos(t), sin(t), 2)
tbounds=(t,0,2*pi)

parametric_plot(r, tbounds)

var('t')
r=(cos(t), sin(t), t)
tbounds=(t,0,4*pi)

parametric_plot(r, tbounds)

# 21 in 13.1
var('t')
r=(t*cos(t), t, t*sin(t))
tbounds=(t,0,10*pi)

parametric_plot(r, tbounds)

# 22 in 13.1
var('t')
r=(cos(t), sin(t), 1/(1+t^2))
tbounds=(t,-4*pi,4*pi)

parametric_plot(r, tbounds)

# 23 in 13.1
var('t')
r=(t, 1/(1+t^2), t^2)
tbounds=(t,-20,20)

parametric_plot(r, tbounds)

# 24 in 13.1
var('t')
r=(cos(t), sin(t), cos(2*t))
tbounds=(t,-4*pi,4*pi)

parametric_plot(r, tbounds)

# 25 in 13.1
var('t')
r=(cos(8*t), sin(8*t), e^(0.8*t))
tbounds=(t,0,pi)

parametric_plot(r, tbounds)

# 26 in 13.1
var('t')
r=((cos(t))^2, (sin(t))^2, t)
tbounds=(t,-2*pi,2*pi)

parametric_plot(r, tbounds)