#include <library.h>

/*
           1      3      5      7      9      11      13      15
          X      X      X      X      X      X       X       X
sin(X) =  --  -  --  +  --  -  --  +  --  -  ---  +  ---  -  ---  + ... 
          1!     3!     5!     7!     9!     11!     13!     15!
*/


double power(const double a, const int p)
{ if (p == 0)
    return 1;
  else
    return a * power(a, p - 1); }

double factorial(const int n)                  // WHY DOUBLE AND NOT INT ?????
{ if (n == 0)
    return 1;
  else
    return n * factorial(n - 1); }

int plusminus(const int i)
{ const int rem = i % 4;
  if (rem == 1)
    return +1;
  else if (rem == 3)
    return -1;
  else
    return 0; }

double sine_approx(const double x, const int last_N)
{ if (last_N < 0)
    return 0;
  const double previous_terms = sine_approx(x, last_N - 1);
  const double last_term = power(x, last_N) / factorial(last_N) * plusminus(last_N);
  return previous_terms + last_term; }

const double pi = acos(-1.0);

double degrees_to_radians(const double a)
{ return pi * a / 180.0; }

void main()
{ cout << "Last term? ";
  const int N = read_int();
  while (true)
  { cout << "x? ";
    const double x = degrees_to_radians( read_double() );
    cout << "correct = " << setprecision(16) << sin(x) << "\n";
    cout << " approx = " << setprecision(16) << sine_approx(x, N) << "\n"; } }