CosineTaylorSeries.java

package day3;

import java.util.Scanner;

public class CosineTaylorSeries {
    /*
        cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ....

        a(i) = (-1)^î * x^(2i) / (2i)!

        oscillation *= -1 initaial_value = 1
        factor *= x^2 initial_value = 1
        factorial = (2i + 2)(2i + 1) initial_value = 0! = 1

        i = 1
        2! * 3 * 4 = 4!

        i = 2
        4! * 5 * 6 = 6!

        i
        (2i)!* (2i + 1) * (2i + 2) = (2i + 2)!
     */

    // time complexity: O(1)
    // space complexity: O(1)
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        double theta = scanner.nextDouble();
        double result = 0;

        for (double precision = 0, oscillation = 1, factor = 1, factorial = 1 ; precision < 10 ; precision++) {
            result += oscillation * factor / factorial;
            oscillation *= -1;
            factor *= theta * theta;
            factorial *= (2 * precision + 1) * (2 * precision + 2);
        }

        System.out.println(result);
    }
}