[hardwired]

Code:

public class NRTest {
    public static void main(String[] args) {
        NewtonRaphson f = new NewtonRaphson();
        double x = 2;
        double root = f.solve(x);
        //System.out.println("root = " + root);
    }
}

class NewtonRaphson {
    // Our approximation of zero
    final double TOLERANCE = .000000005;
    // Maximum number of Newton's method iterations
    final int MAX_COUNT = 200;

    // f(x) = cos(x)
    private double f(double x) {
       return Math.sin(x);
    }

    // f'(x) = sin(x)
    private double fprime(double x) {
        return Math.cos(x);
    }

    public double solve(double x0) {
        System.out.printf(" %-8s%-13s%-12s%-16s%-15s%s%n",
                          "n", "x_n", "f(x_n)", "f'(x_n)", "x_n+1", "dx");
        double x = x0;
        int n = 0;
        do {
            x = x0 - f(x)/fprime(x);
            double dx = x - x0;
            System.out.printf("%2d   %10f    %10f   %10f    %10f    %10f%n",
                               n, x0, f(x), fprime(x), x, dx);
            x0 = x;
            if(Math.abs(dx) < TOLERANCE)
                break;
        } while(++n < MAX_COUNT);

        if( Math.abs(f(x)) <= TOLERANCE) {
            System.out.println("Zero found at x="+x);
        } else {
            System.out.println("Failed to find a zero");
        }
        return x;
    }
}