import numpy as np
x = np.linspace(-100,100,10000)
y = np.sin(x)
plt.plot(x,y,'g-.')
plt.xlim(-np.pi,np.pi)
fig,ax = plt.subplots()
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z ** 2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
ax.plot(x, y, label='parametric curve')
ax.legend()