Question

The shape of a limacon can be defined parametrically as

                                   r = r0 + cos θ,

                                   x = r cos θ,

                                   y = r sin θ.

When r0 = 1, this curve is called a cardioid. Use this definition to plot the shape of a limacon for r0 = 0.8, r0 = 1.0, and r0 = 1.2. Be sure to use enough points that the curve is closed and appears smooth (except for the cusp in the cardioid). Use a legend to identify which curve is which. This is python programming

Answer 1

import matplotlib.pyplot as plt
import math
from matplotlib.pyplot import figure
#Set figure size
figure(num=None, figsize=(5,10))
r_values = [0.8, 1.0, 1.2]
#We will create subplots in 3x1 arrangement
for j in range(1,4):
    ax = plt.subplot(3,1, j)     #3,1,j means 3rd row, 1st column, jth subplot
    #Set title for jth subplot
    ax.set_title(str(r_values[j-1]))
    x = []        #Empty lists that will store values of x and y
    y = []
    #Generating x and y values according to r and theta as given in equation
    for theta in range(0,360):
        r = r_values[j-1] + math.cos(theta)
        x.append(r*math.cos(theta))
        y.append(r*math.sin(theta))
        #Plot x,y points
        plt.scatter(x, y, color='r')