12.1: Math Methods

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In mathematics, you have probably seen functions like sin and log, and you have learned to evaluate expressions like \( \sin(\pi/2) \) and \( \log{(1/x)} \). First, you evaluate the expression in parentheses, which is called the argument of the function. Then you can evaluate the function itself, maybe by punching it into a calculator.

This process can be applied repeatedly to evaluate more complex expressions like \( \log{(1 / \sin(\pi/2))} \). First we evaluate the argument of the innermost function, then evaluate the function itself, and so on.

The Java library includes a Math class that provides common mathematical operations. Math is in the java.lang package, so you don’t have to import it. You can use, or invoke, Math methods like this:

double root = Math.sqrt(17.0);
double angle = 1.5;
double height = Math.sin(angle);

The first line sets root to the square root of 17. The third line finds the sine of 1.5 (the value of angle).

Arguments of the trigonometric functions – sin, cos, and tan – should be in radians. To convert from degrees to radians, you can divide by 180 and multiply by π. Conveniently, the Math class provides a constant double named PI that contains an approximation of \( \pi \):

double degrees = 90;
double angle = degrees / 180.0 * Math.PI;

Notice that PI is in capital letters. Java does not recognize Pi, pi, or pie. Also, PI is the name of a variable, not a method, so it doesn’t have parentheses. The same is true for the constant Math.E, which approximates Euler’s number.

Converting to and from radians is a common operation, so the Math class provides methods that do it for you.

double radians = Math.toRadians(180.0);
double degrees = Math.toDegrees(Math.PI);

Another useful method is round, which rounds a floating-point value to the nearest integer and returns a long. A long is like an int, but bigger. More specifically, an int uses 32 bits; the largest value it can hold is 2³¹−1, which is about 2 billion. A long uses 64 bits, so the largest value is 2⁶³−1, which is about 9 quintillion.

long x = Math.round(Math.PI * 20.0);

The result is 63 (rounded up from 62.8319).

Take a minute to read the documentation for these and other methods in the Math class. The easiest way to find documentation for Java classes is to do a web search for “Java” and the name of the class.