Polar plots.sagews

%auto

var('r, theta')

(r, theta)

$r = \cos{(2\theta)}, \quad 0 \leq \theta \leq 2\pi$

polar_plot(cos(2*theta), (theta, 0, 2*pi))

$r = \cos{(3\theta)}, \quad 0 \leq \theta \leq \pi$

polar_plot(cos(3*theta), (theta, 0, pi))

r = theta
polar_plot(r, (theta, 0, 10))

$r = \log{\theta}, \quad 0 \leq \theta \leq 30\pi$

r= log(theta)
polar_plot(r, (theta, 1, 30*pi), plot_points = 1000)

for n in range(-6,7):
    r = 1 + (n/2) * sin(theta);
    polar_plot(r, (theta, 0, 2*pi))

"Heart to Bell"

$r = \cos{(5\theta)} + \frac{n}{2}\cos{\theta}, \quad 0 \leq \theta \leq \pi$

for values of $n$ between -10 and 10.

for n in range(-10, 11):
    r = cos(5 * theta) + (n/2) * cos(theta);
    polar_plot(r, (theta, 0, pi))

r = 1 - cos(1.01 * theta) - 0.2 * cos(8 * theta)
polar_plot(r, (theta, 0, 400*pi), plot_points = 8000, figsize = 8, thickness = 0.2)

r = exp(sin(theta)) - 2 * cos(4 * theta);
polar_plot(r, (theta, 0, 2*pi), figsize = 8)

r = exp(sin(theta)) - 2 * cos(4 * theta) + (sin(theta/12))^5
polar_plot(r, (theta, 0, 24*pi), figsize = 8)