{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pylab as plt\n",
    "import math\n",
    "\n",
    "R=5\n",
    "\n",
    "def f(theta31):\n",
    "    return (theta21**2+theta31**2-R**2)\n",
    "\n",
    "def Dichotomie(f,a,b,eps):\n",
    "    if f(b)*f(a)>=0:return None\n",
    "    while b-a > eps:\n",
    "        c = (a+b)/2.0\n",
    "        if f(a) * f(c) < 0: b = c\n",
    "        else: a = c\n",
    "    return a\n",
    "\n",
    "abscisse = np.linspace(-5, 5, 100)\n",
    "ordonnee_dicho=[]\n",
    "\n",
    "for i in range(len(abscisse)):\n",
    "    theta21=abscisse[i]\n",
    "    ordonnee_dicho.append(Dichotomie(f, -0, 10, 0.001))\n",
    "\n",
    "\n",
    "plt.plot(abscisse, ordonnee_dicho)\n",
    "plt.grid(True)\n",
    "plt.xlabel('$\\Theta 21$ en rad')\n",
    "plt.ylabel('$\\Theta 31$ en rad')\n",
    "plt.title('loi entree sortie')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
