//------------------------------------------------------------
// Purpose: Program to calculate Taylors series approximations
//          of sin(x) and cos(x) with varying number of terms.
// Author:  John Gauch
//------------------------------------------------------------

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

void print_sin_table(double x, int num_terms, int width)
{
   // local variables
   double n_factorial = 1;
   double x_to_n = 1;
   double taylor_term = 0;
   double sin_x = 0;

   // print table header
   cout << endl 
        << setw(width) << "n"
        << setw(width) << "x^n/n!" 
        << setw(width) << "sin(x)" 
        << endl;

   // loop over num_terms
   for (int n = 1; n <= num_terms; n++)
   {
      // calculate taylor_term
      n_factorial = n_factorial * n;
      x_to_n = x_to_n * x;
      taylor_term = x_to_n / n_factorial;

      // add to sin_x taylors series
      if (n % 4 == 1)
         sin_x = sin_x + taylor_term;
      else if (n % 4 == 3)
         sin_x = sin_x - taylor_term;

      // Print variables
      cout << setw(width) << n 
           << setw(width) << taylor_term 
           << setw(width) << sin_x 
           << endl;
   }

   // perform error analysis
   cout << endl;
   cout << "estimated sin: " << sin_x << endl;
   cout << "true sin:      " << sin(x) << endl;
   cout << "sin error:     " << sin_x - sin(x) << endl;
}

void print_cos_table(double x, int num_terms, int width)
{
   // local variables
   double n_factorial = 1;
   double x_to_n = 1;
   double taylor_term = 0;
   double cos_x = 1;
   int sign = 1;

   // print table header
   cout << endl 
        << setw(width) << "n"
        << setw(width) << "x^n/n!" 
        << setw(width) << "cos(x)" 
        << endl;

   // loop over num_terms
   for (int n = 1; n <= num_terms; n++)
   {
      // calculate taylor_term
      n_factorial = n_factorial * n;
      x_to_n = x_to_n * x;
      taylor_term = x_to_n / n_factorial;

      // add to cos_x taylors series
      if (n % 2 == 0)
      {
         sign = -sign;
         cos_x = cos_x + taylor_term * sign;
      }

      // Print variables
      cout << setw(width) << n 
           << setw(width) << taylor_term 
           << setw(width) << cos_x 
           << endl;
   }

   // perform error analysis
   cout << endl;
   cout << "estimated cos: " << cos_x << endl;
   cout << "true cos:      " << cos(x) << endl;
   cout << "cos error:     " << cos_x - cos(x) << endl;
}

int main()
{
   // local variables
   int width = 15;
   double x = 0;
   int num_terms = 0;
   double n_factorial = 1;
   double x_to_n = 1;

   // read user input
   cout << "Enter angle in radians: ";
   cin >> x;
   cout << "Enter number of terms: ";
   cin >> num_terms;

   // print first table
   cout << setw(width) << "n"
        << setw(width) << "n!" 
        << setw(width) << "x^n" 
        << endl;

   // loop over num_terms
   for (int n = 1; n <= num_terms; n++)
   {
      // calculate taylor_term
      n_factorial = n_factorial * n;
      x_to_n = x_to_n * x;

      // Print variables
      cout << setw(width) << n 
           << setw(width) << n_factorial 
           << setw(width) << x_to_n 
           << endl;
   }

   // print two more tables
   print_sin_table(x, num_terms, width);
   print_cos_table(x, num_terms, width);

   return 0;
}