Arithmetic expressions containing Mathematical functions

Arithmetic expressions containing Mathematical functions

Scientific calculations often involve Mathematical functions, such as sin, cos, tan, log, and so on.
Examples: sin and ln functions on a calculator

Programming languages allow you to embed Mathematical functions within a arithmetic expression.

Furthermore, a computer allows you to use variables as arguments to a Mathematical function

In other words:

Suppose you have define a variable x as follows:

You can write expressions like these:

sin(x) computes the sin of x sin(2*x) computes the sin of 2*x

Note:

Java's function library

The Java programming language has an extensive collection of functions (methods) organized in various libraries

Note: a bit of history

In Mathematics, the sin() operation is called a function
In Java, the sin() operation is implemented by a Java method
In fact, we used the words "function" and "method" interchangeably in Computer Science.
Before the word method became popular, other words used were:

The documentation of the Java methods (functions) are online at the following website: click here
We will now look at the Mathematical functions which are documented on this webpage: click here

Java's Mathematical functions (methods)

Here are some of the names of Java's Mathematical functions (methods):

Java's method name	Corresponding Mathematical function
`Math.sin(x)`	Sine function of value `x`
`Math.cos(x)`	Cosine function of value `x`
`Math.tan(x)`	Tangent function of value `x`
`Math.asin(x)`	Arc sine (inverse of sine) function of value `x`
`Math.acos(x)`	Arc cosine function of value `x`
`Math.atan(x)`	Acr tangent function of value `x`
`Math.exp(x)`	e^x
`Math.log(x)`	Natural log function of value `x`
`Math.log10(x)`	10-based log function of value `x`
`Math.pow(a, b)`	`a^b`
`Math.sqrt(x)`	Squared root of the number `x`

Using Java's Mathematical functions

Example: compute √2

You can apply a Mathematical function on a floating point variable

Examples:

double a; Math.sqrt(a) will compute the squared root on the value that is current stored in the variable a Math.sqrt(a+1) will compute the squared root on the value a+1

A note on "computing values" in a computer program

We just learned how to compute √2

Consider the following Java program:

public class CompVal { public static void main(String[] args) { Math.sqrt(2.0); // Computes √2 } }

Interesting result:

When you compile and run this program, you will see .... absolutely nothing !!!

Example Program: (Demo above code)
- Prog file: click here
How to run the program:

The reason is:

Unlike a calculator that always shows the result of a computation on its display....
A computer will only show the result of a computation when it is told !!!

Example:

public class CompVal2 { public static void main(String[] args) { System.out.println( Math.sqrt(2.0) ); // Print !! } }

This program will print: 1.4142135623730951 (which is the decimal value of √2)

Programming facts:

A computed value is not printed
If you want to print a computed value, use a print statement
A computed value is not stored
If you want to store (save) a computed value, use an assignment statement

Example: storing a computed value

public class CompVal3 { public static void main(String[] args) { double a; a = Math.sqrt(2.0); // Save computed value in variable System.out.println(a); // You can print the saved value later } }

A real-life example: programming the a,b,c-formula

Quadratic equation:
Solutions:

The Mathematical expressions are written in Java as follows:

written as: ( -b - Math.sqrt( b*b - 4*a*c ) ) / (2*a)
written as: ( -b + Math.sqrt( b*b - 4*a*c ) ) / (2*a)

Here is a Java program to compute the famous a,b,c-formula:

public class Abc { public static void main(String[] args) { double a, b, c, x1, x2; // Define 5 variable a = 1.0; b = 0.0; c = -4.0; x1 = ( -b - Math.sqrt( b*b - 4*a*c ) ) / (2*a); x2 = ( -b + Math.sqrt( b*b - 4*a*c ) ) / (2*a); System.out.print("a = "); System.out.println(a); System.out.print("b = "); System.out.println(b); System.out.print("c = "); System.out.println(c); System.out.print("x1 = "); System.out.println(x1); System.out.print("x2 = "); System.out.println(x2); } }

Example Program: (Demo above code)
- Prog file: click here
How to run the program: