/*--------------------------------------------------------------------*/ 
/*  Problem chapter3_102                                              */ 
/*                                                                    */ 
/*  Newton's formula for a root of x^2=cos(x)                           */ 
 
#include <iostream> 
#include <cmath>
using namespace std; 
 
int main() 
{ 
   double a; 
 
   cout << "Enter an initial approximation between 0 and 1: ";
   cin >> a ;
 
   while ( fabs(a*a-cos(a))>1e-5 )
      a -= (a*a-cos(a))/(2.0*a+sin(a)); 

   cout << " the root is " << a << endl; 
 
   //  Exit program.  
   return 0; 
}