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

double f ( double x ) {
  return sin(x);
}

double f_prime ( double x ) {
  return cos(x);
}


int main() {
  double x, xp;
  double delta = 0.01;

  x = 3;
  xp =  x - f(x)/f_prime(x);

  printf("x: %f   x': %f\n", x, xp);

  while ( fabs( x - xp ) >= delta ) {
    x = xp;
    xp = x - f(x)/f_prime(x);

    printf("x: %f   x': %f\n", x, xp);

  }

  printf("Approximate root: %f\n", xp);

  return 0;
}