#include <math.h>
#include <stdio.h>

// calculul sinusului pana la un anumit termen
double sinus_n(double x, unsigned n)
{
  unsigned k = 1;
  double s = 0, t = x;
  while (k <= n) {
    s += t;
    k += 2;
    t *= -x*x/k/(k-1);
  }
  return s;
}

// calculul sinusului pana termenul e mai mic decat o precizie data
double sinus(double x, double prec)
{
  unsigned k = 1;
  double s = 0, t = x;
  while (fabs(t) >= prec) {
    s += t;
    k += 2;
    t *= -x*x/k/(k-1);
  }
  return s;
}

int main(void)
{
  printf("%f\n", sinus_n(1, 10));
  printf("%f\n", sinus(1, 1e-6));
  printf("%f\n", sin(1));
  return 0;
}