Identidad trigonometrica en Julia.

Identidad_Trigonometrica.ipynb

{
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  "name": ""
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 "worksheets": [
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Identidad trigonometrica.\n",
      "\n",
      "####Ismael Venegas Castell\u00f3: <ismael.vc1337@gmail.com>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Usando IJulia."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Una identidad trigonometrica esta dada por:\n",
      "\n",
      "$cos^2\\frac{x}{2} = \\frac{tanx + sinx}{2tanx}$\n",
      "\n",
      "Verificar que la identidad es correcta calculando\n",
      "cada lado de la ecuaci\u00f3n, siendo $x = \\frac{\\pi}{5}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = pi/5\n",
      "\n",
      "println(\"x = $x\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "x = 0.6283185307179586\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Primero calcular el lado izquierdo de la ecuaci\u00f3n:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lado_izq = cos(x/2)^2\n",
      "\n",
      "println(\"El lado izquierdo equivale a: $lado_izq\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "El lado izquierdo equivale a: 0.9045084971874736\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Despues calcular el lado derecho:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lado_der = (tan(x) + sin(x)) / 2tan(x)\n",
      "\n",
      "println(\"El lado derecho equivale a: $lado_der\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "El lado derecho equivale a: 0.9045084971874736"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Por ultimo comprobamos la igualdad:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "if lado_izq == lado_der\n",
      "    println(\"La identidad es correcta.\")\n",
      "else\n",
      "    println(\"La identidad es incorrecta.\")\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "La identidad es correcta.\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
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}