How do I plot a cycloid parametrically?

Question

I'm in a beginning python class and I'm supposed to plot this cycloid using subplots. I was given the cycloid in parametric form and told to leave it in that form.

Here are the equations I was given:

x = r (θ − sin θ )

y = r (1 − cos θ )

r is supposed to be a user input into my function.

I don't understand how to define theta, or how to plot parametrically. thank you so much!!

Here's the code I have so far:

import matplotlib.pyplot as plt 
import sympy as sp

def cycloid(r):
    x = r(theta - sp.sin(theta))
    y = r(1 - sp.cos(theta))
    sp.plot_parametric(x, y, (r, -2*sp.pi, 2*sp.pi))
    plt.show()

cycloid(5)

Answer 1

# Various imports
import matplotlib.pyplot as plt
from math import sqrt, cos, sin
import numpy as np

def cycloid(r):
  x = [] #create the list of x coordinates
  y = [] #create the list of y coordinats
  for theta in np.linspace(-2*np.pi, 2*np.pi, 100): #loop over a list of theta, which ranges from -2π to 2π
    x.append(r*(theta - sin(theta))) #add the corresponding expression of x to the x list
    y.append(r*(1 - cos(theta))) #same for y
  plt.plot(x,y)  #plot using matplotlib.piplot
  plt.show()  #show the plot

cycloid(5) #call the function

You can change the resolution of the plot by changing the "100" in the np.linspace parameters. Try to set it to very low (5) then very high (1000) to see the difference.