tp_13.py

from math import exp, sqrt, log, cos, sin, pi

import numpy as np
import matplotlib.pyplot as plt

plt.rcParams["savefig.dpi"] = 500

## Exercice 3
def suite(f, u, n, a, b, c, d):
  x = [u, u]
  y = [0, f(u)]
  for i in range(1, n+1):
    u = f(u)
    x = x+[u, u]
    y = y+[u, f(u)]
  plt.plot(x, y, 'r-', lw=2) # la ligne brisé
  plt.plot([a,b],[0,0],'k') #abscisses
  plt.plot([0,0],[c,d],'k') #ordonnées
  plt.plot(
    [min(a, c), min(b, d)],
    [min(a,c), min(b, d)]
  ) # 1ere bissectrice
  t = np.arange(a, b, 0.01)
  T = np.vectorize(f)(t)
  plt.plot(t, T, 'b-', lw=2)
  plt.xlim(a, b)
  plt.ylim(c, d)
  
#suite(np.cos, 1.4, 10, 0, 1.6, 0, 1)
#suite(lambda x: np.sin(x)/2, 1, 10, 0, 1.6, 0, 1)
#suite(lambda x: 1/4 * (x+1)**2, -1.9, 10, -2, 2, 0, 2)
#suite(lambda x: 1/4 * (x+1)**2, 1.5, 9, 0, 7, 0, 12)

## Exercice 4

def superPlot(xFun, yFun, tMin, tMax):
  t = np.arange(tMin, tMax, 0.01)
  x = np.vectorize(xFun)(t)
  y = np.vectorize(yFun)(t)
  plt.plot(x, y)

plt.subplot(2, 2, 1)
superPlot(
  lambda t: sin(t)**3,
  lambda t: cos(t)-cos(t)**4,
  0, 2*pi
)

plt.subplot(2, 2, 2)
superPlot(
  lambda t: 3*cos(t)+2*cos(3*t),
  lambda t: 3*sin(t)-2*sin(3*t),
  0, 2*pi
)

plt.subplot(2, 2, 3)
superPlot(
  lambda t: cos(t)*(1-2*cos(t)),
  lambda t: sin(t)*(1-2*cos(t)),
  0, 2*pi
)

plt.subplot(2, 2, 4)
superPlot(
  lambda t: cos(t)+sqrt(8)*cos(t/2),
  sin,
  0, 4*pi
)

plt.show()