/* compute cos(x) using the first 5 terms of the series. */

#include <iostream>
#include <cmath>
using namespace std;

double approx(double);
int fact(int);

int main( )
{ double x;
  cout << "Enter the value of x: "<<endl;
  cin >> x;
  cout << "The value of cos(x) using C++ library function is: " << cos(x) << endl;
  cout << "The value of cos(x) using the first 5 terms of the series is: " << approx(x) << endl;
  return 0;
}

double approx(double x)  //compute cos(x) using the first 5 terms of the series
{ double y;
  y = 1.0 - pow(x,2)/fact(2) + pow(x,4)/fact(4) - pow(x,6)/fact(6) + pow(x,8)/fact(8);
  return y;
}

int fact(int n)  // compute n!
{ int nfact=1;
  while (n>1)
   {nfact = nfact * n;
    n--;
   }
  return nfact;
}