Question

* This is for CS 101 Java class. I can only use "while" loops. I cannot use "for", "do-while" or any other repetition method.*

d. Create a new project Lab04d. In this part, you are going to compute arctan(x) in radians The following formula approximates the value of arctan(x) using Taylor series expansion: 2k +1 tan-1 (x) = > (-1)" 2k 1 k=0 Depending on the number of terms included in the summation the approximation becomes more accurate Your program will input from the user the value of x, which should be in the range (-1,1) and also the precision of the summation. You are going to calculate how many terms of the series are needed to approximate the sum up to the given precision for the given x value Since it is an alternating series, the absolute error of the approximation of arctan(x) by the 2k+1 partial sum, Σ-o(-1)" 2k +1 72 lx2n+3 2k + 11-2n+3 2k+1 2k+1 tan-1(x)-〉 (-1)" 2k +1 k=0 k =n+ 1 that is the absolute value of the (n+1)st term in the series. If this is bounded by absolute error of the approximation is desired to be less than some precision > 0, then it is - precision 2n+3 sufficient to set n to be smallest integer n such that

Answer 1

import java.util.Scanner;

public class arctan {

public static void main(String[] args) {

Scanner input = new Scanner(System.in);

double x, error, precision, steps=0, sum = 0;

System.out.print("Enter x: ");

x=input.nextDouble();

System.out.print("Enter precision: ");

precision=input.nextDouble();

error=1;

while (error>precision)

{

sum=sum+Math.pow(-1, steps)*(Math.pow(x, 2*steps+1))/(2*steps+1);

System.out.print("\nCurrent sum: "+sum);

error=(Math.pow(Math.abs(x), 2*steps+2))/(2*steps+3);

steps+=1;

}

System.out.printf("\n\nComputed with %.1e precision in %.0f steps\n", precision,steps);

System.out.printf("arctan("+x+") = "+sum+" radians");

input.close();

}

}

Enter x:76 Enter precision: .0001 Current sum: 0.76 Current sum: 0.6136746666666667 Current sum 0.6643851741866666 Current sum 0.6434634676555581 Current sum: 0.6528624280829557 Current sum 0.6484206502751572 Current sum: 0.6505915179274363 Current sum: 0.6495048105256074 Current sum 0.6500586477567513 Current sum: 0.6497724246756961 Current sum 0.6499220021319214 Current sum: 0.6498431188835287 Computed with 1.0e-04 precision in 12 steps arctan(0.76) - 0.6498431188835287 radians