{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week 9 Notes: Numeric Methods using loops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999980926513672\n"
     ]
    }
   ],
   "source": [
    "approx = 0\n",
    "\n",
    "for i in range(1,20):\n",
    "    term = 1/2**i\n",
    "    approx = approx + term\n",
    "\n",
    "print(approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7853956633974299\n"
     ]
    }
   ],
   "source": [
    "approx = 0\n",
    "\n",
    "for i in range(0,100000):\n",
    "    term = (-1)**i * (1/(2*i+1))\n",
    "    approx = approx + term\n",
    "\n",
    "print(approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7853981633974483"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.pi/4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter a number1.57079\n",
      "0.9999999999799855\n"
     ]
    }
   ],
   "source": [
    "from math import factorial\n",
    "\n",
    "approx = 0\n",
    "x_str = input('Enter a number')\n",
    "x = float(x_str)\n",
    "for i in range(10):\n",
    "    term = ((-1)**i) * ((x**(2*i+1)) / (factorial(2*i+1) ))\n",
    "    #approx = approx + term\n",
    "    approx += term\n",
    "    \n",
    "print(approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999799858"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.sin(1.57079)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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