## Using class Math

Math is yet another class belonging to the core set of the Java programing language. We take a tour on selected methods:

Figure 409. Math.sin(double x)
Code Result Math notation
final double x = 90;
final double y = Math.sin(x);
System.out.println(y + " == sin(" + x + ")");
0.8939966636005579 == sin(90.0)
$y = sin ⁡ x$ No. 133

### Common pitfall using trigonometric functions

 Q: We reconsider Figure 409, “Math.sin(double x) ”. Did you expect a value of 0.8939966636005579 corresponding to an angle of 90° here? Discuss the underlying problem. A: The mathematically inclined reader may have expected a result of 1.000... corresponding to a right angle of 90° rather than 0.893.... This is a common misconception: At school you were probably using so called “degrees” ranging from 0° to 360° for describing angle values. In Mathematics however trigonometric functions are being defined as power series e.g.: $sin ⁡ x = x - x 3 3! + x 5 5! + ... = ∑ n = 0 ∞ ( -1 ) n ⁢ x 2n + 1 ( 2n + 1 ) !$ As an immediate consequence describing a full circle of angle values the variable x here is ranging from 0 to $2 ⁢ π$ rather than from 0° to 360°. This angle unit is called radians. If you still want to use degrees you will have to convert these to radians beforehand by multiplying with $2 ⁢ π 360°$ or simply $π 180$: final double x = 90; final double y = Math.sin(x * Math.PI / 180); //converting degrees to radians System.out.println(y + " == sin(" + x + ")"); No. 134

### Using constants from java.lang.Math.

Q:

In Exercise Calculating a circle's area avoiding accidental redefinition you calculated a given circle's area protecting variables against accidental redefinition using the final modifier:

public static void main(String[] args) {

double radius = 2.31;         // A circle having a radius (given e.g. in mm).
final double PI = 3.1415926;  // Creating PI as a constant (non-modifiable/
// assignable) variable.

System.out.println(area);
}

You may have wondered why you had to punch in the value of such an important constant as $π$ by yourself. Actually Java predefines constants in java.lang.Math class. Read its documentation to rewrite your code thereby replacing your own variable pi's definition .

### Tip

You may want to read the Static Members and Java Packages sections of [Kurniawan].

A:

public static void main(String[] args) {

double radius = 2.31;       // A circle having a radius (given e.g. in mm).

System.out.println(area);
}

In case you bother about using the somewhat clumsy Math.PI expression rather than just using PI itself some syntactic sugar is on offer by means of a static import statement:

import static java.lang.Math.PI;

public class CircleAreaCalculator {

public static void main(String[] args) {

double radius = 2.31; // A circle having a radius (given e.g. in mm).

final double area = PI * radius * radius; // This actually refers to Math.PI
System.out.println(area);
}
}

We dig a little deeper to fully understand the underlying concepts. Obtaining a JDK's source code and browsing its implementation Math.java reveals:

/*
* ...
*/

package java.lang;
...

public final class Math {

...
/**
* The {@code double} value that is closer than any other to
* <i>pi</i>, the ratio of the circumference of a circle to its
* diameter.
*/
public static final double PI = 3.14159265358979323846;
...

This accounts for using the expression Math.PI.

The careful reader may have expected an import statement in order to use the Math class:

import java.lang.Math; // Optional: Classes from java.lang are imported
// implicitely as per the Java language specification.

public class CircleAreaCalculator {

public static void main(String[] args) {

double radius = 2.31; // A circle having a radius (given e.g. in mm).

}
But since the Math class belongs to the java.lang package it is present by default and does not have to be imported.