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  1. {
  2. "cells": [
  3. {
  4. "cell_type": "markdown",
  5. "metadata": {},
  6. "source": [
  7. "# Trigonométrie"
  8. ]
  9. },
  10. {
  11. "cell_type": "markdown",
  12. "metadata": {},
  13. "source": [
  14. "## Le Cercle Trigonométrique\n",
  15. "\n",
  16. "Le cercle trigonométrique est un cercle de rayon 1 centré à l'origine. C'est une manière très pratique de vérifier le signe des fonctions trigonométriques ou de se souvenir rapidement des relations trigonométriques. Par exemple:\n",
  17. "* $\\cos \\alpha + \\pi = -\\cos \\alpha$\n",
  18. "* $\\sin \\alpha + \\pi = -\\sin \\alpha$\n",
  19. "* $-\\sin \\alpha = \\sin -\\alpha$\n",
  20. "* $\\cos \\alpha = \\cos -\\alpha$\n",
  21. "* $\\cos \\alpha-\\frac{\\pi}{2}= \\sin \\alpha$\n",
  22. "* $\\sin \\alpha+\\frac{\\pi}{2}= \\cos \\alpha$"
  23. ]
  24. },
  25. {
  26. "cell_type": "code",
  27. "execution_count": 1,
  28. "metadata": {},
  29. "outputs": [
  30. {
  31. "data": {
  32. "application/vnd.jupyter.widget-view+json": {
  33. "model_id": "4b1201305fb0478d9114ed4f44c15774",
  34. "version_major": 2,
  35. "version_minor": 0
  36. },
  37. "text/plain": [
  38. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  39. ]
  40. },
  41. "metadata": {},
  42. "output_type": "display_data"
  43. },
  44. {
  45. "data": {
  46. "application/vnd.jupyter.widget-view+json": {
  47. "model_id": "f4beb2b4cc634ea080bfe0d155a724f4",
  48. "version_major": 2,
  49. "version_minor": 0
  50. },
  51. "text/plain": [
  52. "interactive(children=(FloatSlider(value=0.6283185307179586, description='Angle:', layout=Layout(height='140px'…"
  53. ]
  54. },
  55. "metadata": {},
  56. "output_type": "display_data"
  57. }
  58. ],
  59. "source": [
  60. "import ipywidgets as widgets\n",
  61. "import numpy as np\n",
  62. "import matplotlib.pyplot as plt\n",
  63. "import matplotlib as mpl\n",
  64. "mpl.style.use('seaborn')\n",
  65. "%matplotlib widget\n",
  66. "pi = np.pi\n",
  67. "t = np.linspace(-2*pi,2*pi,100)\n",
  68. "fig1 = plt.figure(1,figsize=(6, 4))\n",
  69. "fig1.suptitle('Le Cercle Trigonométrique')\n",
  70. "ax1 = fig1.add_subplot(1, 1, 1, aspect=1)\n",
  71. "\n",
  72. "def update_plot(angle):\n",
  73. " ax1.clear()\n",
  74. " ax1.plot(np.cos(t),np.sin(t),color='black')\n",
  75. " theta = np.linspace(0,angle,100)\n",
  76. " ax1.plot(1/6*np.cos(theta),1/6*np.sin(theta),color='gray')\n",
  77. " ax1.axhline(0, color='black', lw=1)\n",
  78. " ax1.axvline(0, color='black', lw=1)\n",
  79. " ax1.axis('equal')\n",
  80. " ax1.plot(np.cos(angle),np.sin(angle))\n",
  81. " ax1.plot([np.cos(angle),np.cos(angle)], [0,np.sin(angle)], color='r', label='Sinus')\n",
  82. " ax1.plot([0,np.cos(angle)], [0,0], color='b', label='Cosinus')\n",
  83. " ax1.plot([1,1], [0,np.tan(angle)], color='g', label='Tangente')\n",
  84. " if(np.tan(angle)!=0):\n",
  85. " cot = 1/np.tan(angle)\n",
  86. " else:\n",
  87. " cot = 0\n",
  88. " ax1.plot([0,cot], [1,1], color='y', label='Cotangente')\n",
  89. " ax1.plot(t,np.tan(angle)*t,color='black',lw=0.8)\n",
  90. " ax1.legend(loc=0)\n",
  91. " ax1.set_xlim(-1.5, 1.5)\n",
  92. " ax1.set_ylim(-1.5, 1.5)\n",
  93. "\n",
  94. "angle = widgets.FloatSlider(min=-2*pi,max=2*pi,step= pi/128,value=pi/5,description='Angle:',readout_format='.1f',layout=widgets.Layout(width='50%', height='140px'))\n",
  95. "widgets.interactive(update_plot, angle=angle)"
  96. ]
  97. },
  98. {
  99. "cell_type": "markdown",
  100. "metadata": {},
  101. "source": [
  102. "***\n",
  103. "## Identité trigonométrique"
  104. ]
  105. },
  106. {
  107. "cell_type": "markdown",
  108. "metadata": {},
  109. "source": [
  110. "$$\\sin{x+y}=\\sin{x}\\cos{y}+\\cos{x}\\sin{y}$$\n",
  111. "$$\\sin{x-y}=\\sin{x}\\cos{y}-\\cos{x}\\sin{y}$$\n",
  112. "$$\\cos{x+y}=\\cos{x}\\cos{y}-\\sin{x}\\sin{y}$$\n",
  113. "$$\\cos{x-y}=\\cos{x}\\cos{y}+\\sin{x}\\sin{y}$$\n",
  114. "$$\\cos^2+\\sin^2=1$$\n",
  115. "$$\\tan{x}=\\frac{\\sin{x}}{\\cos{x}}$$\n",
  116. "$$\\cot{x}=\\frac{\\cos{x}}{\\sin{x}}$$\n",
  117. "$$\\tan{x+y} = \\frac{\\tan{x}+\\tan{y}}{1-\\tan{x}\\tan{y}}$$\n",
  118. "$$\\tan{x-y} = \\frac{\\tan{x}-\\tan{y}}{1+\\tan{x}\\tan{y}}$$\n",
  119. "$$\\sin{x+\\frac{\\pi}{2}}=\\cos{x}$$\n",
  120. "$$\\cos{x-\\frac{\\pi}{2}}=\\sin{x}$$\n",
  121. "$$\\sin{-x}=-\\sin{x}$$\n",
  122. "$$\\cos{x}=\\cos{-x}$$"
  123. ]
  124. },
  125. {
  126. "cell_type": "markdown",
  127. "metadata": {},
  128. "source": [
  129. "***\n",
  130. "## Fonctions\n",
  131. "\n",
  132. "### Sinus\n",
  133. "\n",
  134. "Dans un triangle rectangle, il est le rapport $\\frac{\\text{opposé}}{\\text{hypothénuse}}$.\n",
  135. "\n",
  136. "En fonction de l'angle $x$ en radian, c'est une fonction périodique.\n",
  137. "\n",
  138. "Il est bijectif sur l'interval $D = \\left[-\\frac{\\pi}{2}, +\\frac{\\pi}{2}\\right]$ et se projette sur l'image $I = \\left[-1, +1\\right]$"
  139. ]
  140. },
  141. {
  142. "cell_type": "code",
  143. "execution_count": 2,
  144. "metadata": {
  145. "jupyter": {
  146. "source_hidden": true
  147. }
  148. },
  149. "outputs": [
  150. {
  151. "data": {
  152. "application/vnd.jupyter.widget-view+json": {
  153. "model_id": "dde2e976aadf4ade82abaefa6fcdf167",
  154. "version_major": 2,
  155. "version_minor": 0
  156. },
  157. "text/plain": [
  158. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  159. ]
  160. },
  161. "metadata": {},
  162. "output_type": "display_data"
  163. },
  164. {
  165. "data": {
  166. "text/plain": [
  167. "<matplotlib.legend.Legend at 0x7f0d2baf1f98>"
  168. ]
  169. },
  170. "execution_count": 2,
  171. "metadata": {},
  172. "output_type": "execute_result"
  173. }
  174. ],
  175. "source": [
  176. "x = np.linspace(-pi/2,pi/2,100)\n",
  177. "fig2 = plt.figure(2,figsize=(5,5))\n",
  178. "ax2 = fig2.add_subplot(1,1,1)\n",
  179. "ax2.plot(x,np.sin(x), label=\"$f(x)= \\sin(x)$\", color='red')\n",
  180. "ax2.axhline(0, color='black', lw=1)\n",
  181. "ax2.axvline(0, color='black', lw=1)\n",
  182. "plt.xticks([-pi/2,0,pi/2],['$-\\pi/2$','$0$','$\\pi/2$'])\n",
  183. "plt.yticks([-1,0,1],['$-1$','$0$','$1$'])\n",
  184. "ax2.axis('equal')\n",
  185. "ax2.set_xlim(-pi/2, pi/2)\n",
  186. "ax2.set_ylim(-1, 1)\n",
  187. "ax2.legend(loc=0)\n"
  188. ]
  189. },
  190. {
  191. "cell_type": "markdown",
  192. "metadata": {},
  193. "source": [
  194. "### Arc Sinus\n",
  195. "\n",
  196. "C'est la fonction inverse du sinus.\n",
  197. "\n",
  198. "Il est bijectif sur l'interval $I = \\left[-1, +1\\right]$ et se projette sur l'ensemble de départ du sinus $D = \\left[-\\frac{\\pi}{2}, +\\frac{\\pi}{2}\\right]$"
  199. ]
  200. },
  201. {
  202. "cell_type": "code",
  203. "execution_count": 3,
  204. "metadata": {
  205. "jupyter": {
  206. "source_hidden": true
  207. }
  208. },
  209. "outputs": [
  210. {
  211. "data": {
  212. "application/vnd.jupyter.widget-view+json": {
  213. "model_id": "dda8c6e38ed94a4d89e2763aa6d3de8c",
  214. "version_major": 2,
  215. "version_minor": 0
  216. },
  217. "text/plain": [
  218. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  219. ]
  220. },
  221. "metadata": {},
  222. "output_type": "display_data"
  223. },
  224. {
  225. "data": {
  226. "text/plain": [
  227. "<matplotlib.legend.Legend at 0x7f0d601d2898>"
  228. ]
  229. },
  230. "execution_count": 3,
  231. "metadata": {},
  232. "output_type": "execute_result"
  233. }
  234. ],
  235. "source": [
  236. "x = np.linspace(-1,1,100)\n",
  237. "fig3 = plt.figure(3,figsize=(5,5))\n",
  238. "ax3 = fig3.add_subplot(1,1,1)\n",
  239. "ax3.axhline(0, color='black', lw=1)\n",
  240. "ax3.axvline(0, color='black', lw=1)\n",
  241. "ax3.plot(x,np.arcsin(x), label=\"$f(x)= asin(x)$\", color='red')\n",
  242. "plt.yticks([-pi/2,0,pi/2],['$-\\pi/2$','$0$','$\\pi/2$'])\n",
  243. "plt.xticks([-1,0,1],['$-1$','$0$','$1$'])\n",
  244. "plt.axis('equal')\n",
  245. "ax3.set_xlim(-1, 1)\n",
  246. "ax3.set_ylim(-pi/2, pi/2)\n",
  247. "ax3.legend(loc=0)"
  248. ]
  249. },
  250. {
  251. "cell_type": "markdown",
  252. "metadata": {},
  253. "source": [
  254. "### Cosinus\n",
  255. "\n",
  256. "Dans un triangle rectangle, il est le rapport $\\frac{\\text{adjacent}}{\\text{hypothénuse}}$.\n",
  257. "\n",
  258. "En fonction de l'angle $x$ en radian, c'est une fonction périodique.\n",
  259. "\n",
  260. "Il est bijectif sur l'interval $D = \\left[0,\\pi\\right]$ et se projette sur l'image $I = \\left[-1, +1\\right]$"
  261. ]
  262. },
  263. {
  264. "cell_type": "code",
  265. "execution_count": 4,
  266. "metadata": {
  267. "jupyter": {
  268. "source_hidden": true
  269. }
  270. },
  271. "outputs": [
  272. {
  273. "data": {
  274. "application/vnd.jupyter.widget-view+json": {
  275. "model_id": "b6806e424f964d70839b5deb4caa7bc6",
  276. "version_major": 2,
  277. "version_minor": 0
  278. },
  279. "text/plain": [
  280. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  281. ]
  282. },
  283. "metadata": {},
  284. "output_type": "display_data"
  285. },
  286. {
  287. "data": {
  288. "text/plain": [
  289. "<matplotlib.legend.Legend at 0x7f0d2ba5aeb8>"
  290. ]
  291. },
  292. "execution_count": 4,
  293. "metadata": {},
  294. "output_type": "execute_result"
  295. }
  296. ],
  297. "source": [
  298. "x = np.linspace(0,pi,100)\n",
  299. "fig4 = plt.figure(4,figsize=(5,5))\n",
  300. "ax4 = fig4.add_subplot(1,1,1)\n",
  301. "ax4.axhline(0, color='black', lw=1)\n",
  302. "ax4.axvline(0, color='black', lw=1)\n",
  303. "ax4.plot(x,np.cos(x), label=\"$f(x)= \\cos(x)$\", color='blue')\n",
  304. "plt.xticks([0,pi/2,pi],['$0$','$\\pi/2$','$\\pi$'])\n",
  305. "plt.yticks([-1,0,1],['$-1$','$0$','$1$'])\n",
  306. "ax4 = plt.gca()\n",
  307. "ax4.set_xlim(0, pi)\n",
  308. "ax4.set_ylim(-1, 1)\n",
  309. "ax4.legend(loc=0)"
  310. ]
  311. },
  312. {
  313. "cell_type": "markdown",
  314. "metadata": {},
  315. "source": [
  316. "### Arc Cosinus\n",
  317. "C'est la fonction inverse du cosinus.\n",
  318. "\n",
  319. "Il est bijectif sur l'interval $I = \\left[-1, +1\\right]$ et se projette sur l'ensemble de départ du cosinus $D = \\left[0,\\pi\\right]$ "
  320. ]
  321. },
  322. {
  323. "cell_type": "code",
  324. "execution_count": 5,
  325. "metadata": {
  326. "jupyter": {
  327. "source_hidden": true
  328. }
  329. },
  330. "outputs": [
  331. {
  332. "data": {
  333. "application/vnd.jupyter.widget-view+json": {
  334. "model_id": "fbb81e5aabf044a4b8a4ff3c66c37646",
  335. "version_major": 2,
  336. "version_minor": 0
  337. },
  338. "text/plain": [
  339. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  340. ]
  341. },
  342. "metadata": {},
  343. "output_type": "display_data"
  344. },
  345. {
  346. "data": {
  347. "text/plain": [
  348. "<matplotlib.legend.Legend at 0x7f0d2b9a8fd0>"
  349. ]
  350. },
  351. "execution_count": 5,
  352. "metadata": {},
  353. "output_type": "execute_result"
  354. }
  355. ],
  356. "source": [
  357. "x = np.linspace(-1,1,100)\n",
  358. "fig5 = plt.figure(5,figsize=(5,5))\n",
  359. "ax5 = fig5.add_subplot(1,1,1)\n",
  360. "ax5.axhline(0, color='black', lw=1)\n",
  361. "ax5.axvline(0, color='black', lw=1)\n",
  362. "ax5.plot(x,np.arccos(x), label=\"$f(x)= acos(x)$\", color='blue')\n",
  363. "plt.yticks([0,pi/2,pi],['$0$','$\\pi/2$','$\\pi$'])\n",
  364. "plt.xticks([-1,0,1],['$-1$','$0$','$1$'])\n",
  365. "ax5.axis('equal')\n",
  366. "ax5.set_ylim(0, pi)\n",
  367. "ax5.set_xlim(-1, 1)\n",
  368. "ax5.legend(loc=0)"
  369. ]
  370. },
  371. {
  372. "cell_type": "markdown",
  373. "metadata": {},
  374. "source": [
  375. "### Tangente\n",
  376. "\n",
  377. "Dans un triangle rectangle, c'est le rapport $\\frac{\\text{opposé}}{\\text{adjacent}}$.\n",
  378. "\n",
  379. "En fonction de l'angle $x$ en radian, c'est une fonction périodique.\n",
  380. "\n",
  381. "Elle est bijectif sur l'interval $D = \\left]-\\frac{\\pi}{2}, +\\frac{\\pi}{2}\\right[$ et se projette sur l'image $I = \\mathbb{R}$"
  382. ]
  383. },
  384. {
  385. "cell_type": "code",
  386. "execution_count": 6,
  387. "metadata": {
  388. "jupyter": {
  389. "source_hidden": true
  390. }
  391. },
  392. "outputs": [
  393. {
  394. "data": {
  395. "application/vnd.jupyter.widget-view+json": {
  396. "model_id": "01d357dee1894fa084e556e46e210f4e",
  397. "version_major": 2,
  398. "version_minor": 0
  399. },
  400. "text/plain": [
  401. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  402. ]
  403. },
  404. "metadata": {},
  405. "output_type": "display_data"
  406. },
  407. {
  408. "data": {
  409. "text/plain": [
  410. "<matplotlib.lines.Line2D at 0x7f0d2b983c88>"
  411. ]
  412. },
  413. "execution_count": 6,
  414. "metadata": {},
  415. "output_type": "execute_result"
  416. }
  417. ],
  418. "source": [
  419. "x = np.linspace(-pi/2,pi/2,100)\n",
  420. "fig6 = plt.figure(6,figsize=(5,5))\n",
  421. "ax6 = fig6.add_subplot(1,1,1)\n",
  422. "ax6.axhline(0, color='black', lw=1)\n",
  423. "ax6.axvline(0, color='black', lw=1)\n",
  424. "ax6.plot(x,np.tan(x), label=\"$f(x)= \\sin(x)$\", color='green')\n",
  425. "plt.xticks([-pi/2,0,pi/2],['$-\\pi/2$','$0$','$\\pi/2$'])\n",
  426. "ax6.axis('equal')\n",
  427. "ax6.set_xlim(-pi/2, pi/2)\n",
  428. "ax6.set_ylim(-3, 3)\n",
  429. "ax6.legend(loc=0)\n",
  430. "ax6.axvline(pi/2, color='grey', lw=1, ls='--')\n",
  431. "ax6.axvline(-pi/2, color='grey', lw=1, ls='--')"
  432. ]
  433. },
  434. {
  435. "cell_type": "markdown",
  436. "metadata": {},
  437. "source": [
  438. "### Arc Tangente\n",
  439. "\n",
  440. "C'est l'inverse de la tangente.\n",
  441. "Son ensemble de départ est $\\mathbb{R}$ et son ensemble d'arrivée est $\\left]-\\frac{\\pi}{2},+\\frac{\\pi}{2}\\right[$"
  442. ]
  443. },
  444. {
  445. "cell_type": "code",
  446. "execution_count": 7,
  447. "metadata": {
  448. "jupyter": {
  449. "source_hidden": true
  450. }
  451. },
  452. "outputs": [
  453. {
  454. "data": {
  455. "application/vnd.jupyter.widget-view+json": {
  456. "model_id": "d082198ac2db48a1992475dd152f6a30",
  457. "version_major": 2,
  458. "version_minor": 0
  459. },
  460. "text/plain": [
  461. "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
  462. ]
  463. },
  464. "metadata": {},
  465. "output_type": "display_data"
  466. },
  467. {
  468. "data": {
  469. "text/plain": [
  470. "<matplotlib.lines.Line2D at 0x7f0d2b8e3c50>"
  471. ]
  472. },
  473. "execution_count": 7,
  474. "metadata": {},
  475. "output_type": "execute_result"
  476. }
  477. ],
  478. "source": [
  479. "x = np.linspace(-3,3,100)\n",
  480. "fig7 = plt.figure(7,figsize=(5,5))\n",
  481. "ax7 = fig7.add_subplot(1,1,1)\n",
  482. "ax7.axhline(0, color='black', lw=1)\n",
  483. "ax7.axvline(0, color='black', lw=1)\n",
  484. "ax7.plot(x,np.arctan(x), label=\"$f(x)= atan(x)$\", color='green')\n",
  485. "plt.yticks([-pi/2,0,pi/2],['$-\\pi/2$','$0$','$\\pi/2$'])\n",
  486. "ax7.axis('equal')\n",
  487. "ax7.set_ylim(-pi/2, pi/2)\n",
  488. "ax7.set_xlim(-3, 3)\n",
  489. "ax7.legend(loc=0)\n",
  490. "ax7.axhline(pi/2, color='grey', lw=1, ls='--')\n",
  491. "ax7.axhline(-pi/2, color='grey', lw=1, ls='--')"
  492. ]
  493. },
  494. {
  495. "cell_type": "markdown",
  496. "metadata": {},
  497. "source": [
  498. "***\n",
  499. "## Valeurs des fonctions trigonométriques\n",
  500. "\n",
  501. "Ce tableau indique la valeur des fonctions $\\sin,\\cos$ et $\\tan$ en fonction de l'angle.\n",
  502. "Il est très facile à construire rapidement si l'on ne connaît pas les valeurs par coeur."
  503. ]
  504. },
  505. {
  506. "cell_type": "markdown",
  507. "metadata": {},
  508. "source": [
  509. "$$\n",
  510. "\\begin{array}{|c|c|c|c|c|c|c|}\n",
  511. "\\hline\n",
  512. " & 0 & \\frac{\\pi}{6} & \\frac{\\pi}{4} & \\frac{\\pi}{3} & \\frac{\\pi}{2} & \\pi \\\\\n",
  513. "\\hline\n",
  514. "\\sin{\\alpha} & 0 & \\frac{\\sqrt{1}}{2} & \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{3}}{2} & 1 & 0 \\\\\n",
  515. "\\hline\n",
  516. "\\cos{\\alpha} & 1 & \\frac{\\sqrt{3}}{2} & \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{1}}{2} & 0 & 1 \\\\\n",
  517. "\\hline\n",
  518. "\\tan{\\alpha} & 0 & \\frac{\\sqrt{3}}{3} & 1 & \\sqrt{3} & \\emptyset & 0 \\\\\n",
  519. "\\hline\n",
  520. "\\end{array}\n",
  521. "$$"
  522. ]
  523. },
  524. {
  525. "cell_type": "markdown",
  526. "metadata": {},
  527. "source": [
  528. "#### Construction\n",
  529. "\n",
  530. "1. Trier les angles remarquables du premier cadrant du plus petit au plus grand sur la première ligne.\n",
  531. "2. *Les sinus sont les premiers* car ils sont au dessus au numérateur dans la fonction $\\tan$. Alors il convient de commencer par eux.\n",
  532. "3. Entrer les valeurs remarquables les plus importantes ( $0,\\frac{\\pi}{2}, \\pi$ ). Elle sont facile à évaluer et elle ne valent que 1 ou 0.\n",
  533. "4. Poser la structure $\\frac{\\sqrt{x}}{2}$ dans les trois colonnes restantes pour le $\\sin$ et le $\\cos$.\n",
  534. "5. Comme *les sinus sont les premiers* on écrit de gauche à droite 1,2,3 et pour les cosinus 3,2,1.\n",
  535. "6. On complète pour $\\tan$ en divisant les $\\sin$ par les $\\cos$"
  536. ]
  537. },
  538. {
  539. "cell_type": "code",
  540. "execution_count": 8,
  541. "metadata": {
  542. "jupyter": {
  543. "source_hidden": true
  544. }
  545. },
  546. "outputs": [],
  547. "source": [
  548. "%matplotlib widget"
  549. ]
  550. }
  551. ],
  552. "metadata": {
  553. "kernelspec": {
  554. "display_name": "Python 3",
  555. "language": "python",
  556. "name": "python3"
  557. },
  558. "language_info": {
  559. "codemirror_mode": {
  560. "name": "ipython",
  561. "version": 3
  562. },
  563. "file_extension": ".py",
  564. "mimetype": "text/x-python",
  565. "name": "python",
  566. "nbconvert_exporter": "python",
  567. "pygments_lexer": "ipython3",
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  572. "nbformat_minor": 4
  573. }
  574.  
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