# -*- coding: utf-8 -*-
"""
Exercice 1-5 :  tracé de courbes et recherche de 
points remarquables

Created on Tue Dec 02 15:34:14 2014

@author: grivet
"""

import numpy as np
import matplotlib.pyplot as plt


def f(t,a):
    return t - a*np.sin(t)
def g(t,a):
    return 1 - a*np.cos(t)

t = np.linspace(-2.0,2.0,500)
plt.subplot(2,1,1)
a = 0.5;
plt.plot(t,f(t,a),"r-")
plt.plot(t,g(t,a),"r-")
a = 1.0
plt.plot(t,f(t,a),"g-")
plt.plot(t,g(t,a),"g-")
a = 1.5
plt.plot(t,f(t,a),"b-")
plt.plot(t,g(t,a),"b-")
plt.subplot(2,1,2)
a = 0.5
plt.plot(f(t,a),g(t,a),"r-")
a = 1.0
plt.plot(f(t,a),g(t,a),"g-")
a = 1.5
plt.plot(f(t,a),g(t,a),"b-")
y = g(t,a)
x = f(t,a)
iy = abs(y) < 0.01
print ('x: ', x[iy])
ix = abs(x) < 0.005
print ('y: ', y[ix])
print ('t: ', t[ix])
plt.show()