/**

* Write a method to compute sin(x) and cos(x) using the following series expansion,

* in a class called TrigonometricSeries. The headers of the methods are:

*

* public static double sin(double x, int numTerms) // x in radians

* public static double cos(double x, int numTerms)

*

* ExerciseBasics_TrigonometricSeries.png

*

* Compare the values computed using the series with the JDK methods

* Math.sin(), Math.cos() at x=0, π/6, π/4, π/3, π/2 using various numbers of terms.

*

* Hints: Avoid generating large numerator and denominator (which may cause

* arithmetic overflow, e.g., 13! is out of int range). Compute the terms as:

*

* ExerciseBasics_TrigonometricSeriesHint.png

*/

package javaexercises.difficult;

public class TrigonometricSeries {

public static void main(String[] args)

{

double x = Math.PI/6;

int numTerms = 10;

TrigonometricSeries aTrigonometricSeries = new TrigonometricSeries();

System.out.println("Calculated values:");

System.out.printf("sin(%1$d) = %2$f \n", (int)Math.round(x*180/Math.PI)

, aTrigonometricSeries.sin(x, numTerms));

System.out.printf("cos(%1$d) = %2$f \n", (int)Math.round(x*180/Math.PI)

, aTrigonometricSeries.cos(x, numTerms));

System.out.println("java.lang.Math values:");

System.out.printf("sin(%1$d) = %2$f \n", (int)Math.round(x*180/Math.PI)

, Math.sin(x));

System.out.printf("cos(%1$d) = %2$f \n", (int)Math.round(x*180/Math.PI)

, Math.cos(x));

}

private double calculateTerm(double x, int numTerms)

{

double term = 1D;

for (int i = numTerms; i > 0; i--) {

term *= x/i;

}

return term;

}

private double sin(double x, int numTerms)

{

double result = 0D;

for (int i = 0; i < numTerms; i++) {

result += (i%2 == 0 ? 1 : -1) * calculateTerm(x, (2*i+1));

}

return result;

}

private double cos(double x, int numTerms)

{

double result = 0D;

for (int i = 0; i < numTerms; i++) {

result += (i%2 == 0 ? 1 : -1) * calculateTerm(x, 2*i);

}

return result;

}

}