/******************************************************************************
 *  Compilation:  javac Sin.java
 *  Execution:    java Sin x
 *
 *  Prints out sin(x) using Taylor expansion.
 *
 *     sin x = x - x^3/3! + x^5/5! - x^7/7! + ...
 *
 *  % java sin  java Sin 0.523598775598299
 *  0.5000000000000002
 *
 *  Note:  sin(pi/6) = sin(0.523598775598299...) = 1/2
 *
 *  We use identity sin(x) = sin(x + 2 PI) to pre-process
 *  x to be between -2 PI and 2 PI. Yes, % works with doubles!
 *
 ******************************************************************************/

public class Sin {

    public static void main(String[] args) {
        double x = Double.parseDouble(args[0]);

        // convert x to an angle between -2 PI and 2 PI
        x = x % (2 * Math.PI);

        // compute the Taylor series approximation
        double term = 1.0;      // ith term = x^i / i!
        double sum  = 0.0;      // sum of first i terms in taylor series

        for (int i = 1; term != 0.0; i++) {
            term *= (x / i);
            if (i % 4 == 1) sum += term;
            if (i % 4 == 3) sum -= term;
        }
        System.out.println(sum);
    }
}