Exponential and Logarithmic Methods and Trigonometric Methods and Random Numbers

The next table lists exponential and logarithmic methods of the Math class.

Exponential and Logarithmic Methods Method Description
double exp(double d) Returns the base of the natural logarithms, e, to the power of the argument.
double log(double d) Returns the natural logarithm of the argument.
double pow(double base, double exponent) Returns the value of the first argument raised to the power of the second argument.
double sqrt(double d) Returns the square root of the argument.

The following program, ExponentialDemo , displays the value of e, then calls each of the methods listed in the previous table on arbitrarily chosen numbers:

public class ExponentialDemo {
public static void main(String[] args) {
double x = 11.635;
double y = 2.76;

System.out.printf("The value of e is %.4f%n", Math.E);
System.out.printf("exp(%.3f) is %.3f%n", x, Math.exp(x));
System.out.printf("log(%.3f) is %.3f%n", x, Math.log(x));
System.out.printf("pow(%.3f, %.3f) is %.3f%n", x, y, Math.pow(x, y));
System.out.printf("sqrt(%.3f) is %.3f%n", x, Math.sqrt(x));
}
}

Here's the output you'll see when you run ExponentialDemo:

The value of e is 2.7183
exp(11.635) is 112983.831
log(11.635) is 2.454
pow(11.635, 2.760) is 874.008
sqrt(11.635) is 3.411

Trigonometric Methods
The Math class also provides a collection of trigonometric functions, which are summarized in the following table. The value passed into each of these methods is an angle expressed in radians. You can use the toRadians method to convert from degrees to radians.

Trigonometric Methods Method Description
double sin(double d) Returns the sine of the specified double value.
double cos(double d) Returns the cosine of the specified double value.
double tan(double d) Returns the tangent of the specified double value.
double asin(double d) Returns the arcsine of the specified double value.
double acos(double d) Returns the arccosine of the specified double value.
double atan(double d) Returns the arctangent of the specified double value.
double atan2(double y, double x) Converts rectangular coordinates (x, y) to polar coordinate (r, theta) and returns theta.
double toDegrees(double d)
double toRadians(double d) Converts the argument to degrees or radians.

Here's a program, TrigonometricDemo , that uses each of these methods to compute various trigonometric values for a 45-degree angle:

public class TrigonometricDemo {
public static void main(String[] args) {
double degrees = 45.0;
double radians = Math.toRadians(degrees);

System.out.format("The value of pi is %.4f%n", Math.PI);
System.out.format("The sine of %.1f degrees is %.4f%n", degrees,
Math.sin(radians));
System.out.format("The cosine of %.1f degrees is %.4f%n", degrees,
Math.cos(radians));
System.out.format("The tangent of %.1f degrees is %.4f%n", degrees,
Math.tan(radians));
System.out.format("The arcsine of %.4f is %.4f degrees %n",
Math.sin(radians),
Math.toDegrees(Math.asin(Math.sin(radians))));
System.out.format("The arccosine of %.4f is %.4f degrees %n",
Math.cos(radians),
Math.toDegrees(Math.acos(Math.cos(radians))));
System.out.format("The arctangent of %.4f is %.4f degrees %n",
Math.tan(radians),
Math.toDegrees(Math.atan(Math.tan(radians))));

}
}



The output of this program is as follows:

The value of pi is 3.1416
The sine of 45.0 degrees is 0.7071
The cosine of 45.0 degrees is 0.7071
The tangent of 45.0 degrees is 1.0000
The arcsine of 0.7071 is 45.0000 degrees
The arccosine of 0.7071 is 45.0000 degrees
The arctangent of 1.0000 is 45.0000 degrees

Random Numbers
The random() method returns a pseudo-randomly selected number between 0.0 and 1.0. The range includes 0.0 but not 1.0. In other words: 0.0 <= Math.random() < 1.0. To get a number in a different range, you can perform arithmetic on the value returned by the random method. For example, to generate an integer between 0 and 9, you would write:

int number = (int)(Math.random() * 10);

By multiplying the value by 10, the range of possible values becomes 0.0 <= number < 10.0.

Using Math.random works well when you need to generate a single random number. If you need to generate a series of random numbers, you should create an instance of java.util.Random and invoke methods on that object to generate numbers.