//------------------------------------------------------------
// Purpose: Program to calculate Taylors series approximations
//          of sin(x) and cos(x) with varying number of terms.
// Author:  John Gauch
//------------------------------------------------------------
#include <cmath>
#include <iostream>
using namespace std;

int main()
{
   // Initialize variables
   float X = 0.1;
   float sinX = 0.0;
   float cosX = 1.0;
   float XtoN = 1.0;
   float Nfact = 1.0;

   // Loop to calculate sin and cos
   for (int N = 1; N <= 7; N++)
   {
      // Calculate Taylor series term
      cout << "N:\t" << N << endl;
      XtoN = XtoN * X;
      cout << "XtoN:\t" << XtoN << endl;
      Nfact = Nfact * N;
      cout << "Nfact:\t" << Nfact << endl;

      // Calculate sin value
      if (N % 4 == 1) sinX = sinX + XtoN/Nfact;
      if (N % 4 == 3) sinX = sinX - XtoN/Nfact;
      cout << "sinX:\t" << sinX << endl;
      cout << "truth:\t" << sin(X) << endl;
      cout << "error:\t" << sinX - sin(X) << endl;

      // Calculate cos value
      if (N % 4 == 0) cosX = cosX + XtoN/Nfact;
      if (N % 4 == 2) cosX = cosX - XtoN/Nfact;
      cout << "cosX:\t" << cosX << endl;
      cout << "truth:\t" << cos(X) << endl;
      cout << "error:\t" << cosX - cos(X) << endl;
      cout << endl;
   }
}