/* compute cos(x) using the terms of the series with absolute value > 0.0001. */

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

double approx(double);
double 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 series approximation is: " << approx(x) << endl;
  return 0;
}

double approx(double x)  //compute cos(x) using terms of the series
{ double y = 1.0;
  double term;
//  int a;
  int k = 1;
  term = pow(-1.0,k) * pow(x,2*k)/fact(2*k);
  while(fabs(term) > 0.0001)
   { y = y + term;
     k = k + 1;
     term = pow(-1.0,k) * pow(x,2*k)/fact(2*k);
//     cout << "term = " << term <<endl;
//     cout << "fact = " << fact(2*k) <<endl; 
//    if (k%10 ==0) cin>> a;
   }
  cout << "the terminal term = " <<term << endl;
  cout << "total number of terms used in the approximation = " << k <<endl; 
  return y;
}

double fact(int n)  // compute n!
{ double nfact=1.0;
  while (n>1)
   {nfact = nfact * n;
    n--;
   }
  return nfact;
}