I am trying to build a program that calculates Taylor series for sin(x). With 0< x < pi/2. Approximation of sin(x) is around the point x0 = 0. e is the max error(or inaccuracy… i don’t know how it’s called). Error(or inaccuracy) is calculated with the formula in the method i call “r”. So r must always be less than e. Finally, n is the number of itterations. For example: for n=5, e=1 and x=pi/5 (0.62831853071), the results should be : sin(pi/5) = 0.5877852522… For n=1 r=0.1974, n=2 r=0.0413, n=3 r=0.0065, n=4 r=8.16*10^(-4), n=5 r=8.54*10^(-5)

import java.lang.Math; import java.util.Scanner; public class hw74 {  public static long factorial(int number) {     long result = 1;      for (int factor = 2; factor <= number; factor++) {         result *= factor;     }      return result; }  static double p(double x, double x0, int n) {      double PT = Math.pow(-1, n) * (Math.pow(x-x0, 2*n+1)/factorial(2*n+1));     return PT; }  static double r(double x, int n) {     double rn = Math.pow(x, n+1)/factorial(n+1);     return Math.abs(rn); }  public static void main(String[] args) {     Scanner sc = new Scanner(System.in);     double x0 = 0;     System.out.println("Give x. ");     double x = sc.nextDouble();     System.out.println("Give E. ");     double e = sc.nextDouble();     System.out.println("Give N. ");     int n = sc.nextInt();     int i = 0;     System.out.println(e<r(x, i) && i<n);     System.out.println(r(x, i));     while((r(x, i)<e) && i<n) {         i++;         System.out.println("N is : "+i);         System.out.println("P is : "+p(x,x0,n));         System.out.println("E is : "+r(x,n));     } }    } 

Thanks in advance.