{ "cells": [ { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "x = np.linspace(-2*np.pi,2*np.pi,256)\n", "c,s = np.cos(x),np.sin(x)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RRzB2rO40PsnlE98Nw6gN/EsplfDr59MNw+itlFr5hy/9t1Jq+sUeR5xbRHAE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\nkyWcoXRpR+7Td6W0zDT8LD9KBuSxP1p4uL7NHWlwkNY1WnM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize = (10,6))\n", "ax.plot(x,c,color='red',lw=2,ls='--')\n", "ax.plot(x,s,color='green',lw=2,ls=':')\n", "ax.set_xticks((-np.pi, -np.pi/2, 0, np.pi/2, np.pi),(r'$-\\pi$', r'$-\\pi/2$', r'$0$', r'$+\\pi/2$', r'$+\\pi$'));\n", "ax.set_yticks((-1, 0, +1),(r'$-1$', r'$0$', r'$+1$'));" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QEwOcP88KJZkITwlHpioTTao14R2FlERH24oUhedWI3qhiK1GipKjyYGhwpC6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\nJTmybvLTEbbBGvZ76t9fXUETGgqVKpm06WNXjtFyaUv2/L3HpO0Wh06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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize = (10,6))\n", "ax.plot(x,c,color='red',lw=2,ls='--',label = 'cosine')\n", "ax.plot(x,s,color='green',lw=2,ls=':',label = 'sine')\n", "# ax.set_xticks((-np.pi, -np.pi/2, 0, np.pi/2, np.pi),(1, 2, 3, 4, 5));\n", "ax.set_xticklabels((r'$-\\pi$', r'$-\\pi/2$', r'$0$', r'$+\\pi/2$', r'$+\\pi$'));\n", "# ax.set_yticks((-1, 0, +1),(r'$-1$', r'$0$', r'$+1$'));\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.spines['bottom'].set_position(('data',0))\n", "ax.yaxis.set_ticks_position('left')\n", "ax.spines['left'].set_position(('data',0))\n", "ax.legend(loc='lower left')\n", "\n", "t = 2*np.pi/3\n", "ax.plot([t,t],[0,np.cos(t)], color ='blue', linewidth=2.5, linestyle=\"--\")\n", "ax.scatter([t,],[np.cos(t),], 1000, color ='blue')\n", "\n", "ax.annotate(r'$\\sin(\\frac{2\\pi}{3})=\\frac{\\sqrt{3}}{2}$',\n", " xy=(t, np.sin(t)), xycoords='data',\n", " xytext=(+10, +30), textcoords='offset points', fontsize=16,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=.2\"))\n", "\n", "ax.plot([t,t],[0,np.sin(t)], color ='red', linewidth=2.5, linestyle=\"--\")\n", "ax.scatter([t,],[np.sin(t),], 50, color ='red')\n", "\n", "ax.annotate(r'$\\cos(\\frac{2\\pi}{3})=-\\frac{1}{2}$',\n", " xy=(t, np.cos(t)), xycoords='data',\n", " xytext=(0, -90), textcoords='offset points', fontsize=16,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=.2\"));\n", "\n", "for label in ax.get_xticklabels() + ax.get_yticklabels():\n", " label.set_fontsize(16)\n", " label.set_bbox(dict(facecolor='white', edgecolor='None', alpha=0.65 ))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }