Lesson 11: Mathematical Functions

The mathematical functions are very useful and important in programming because very often we need to deal with mathematical concepts in programming such as chance and probability, variables, mathematical logics, calculations, coordinates, time intervals and etc. The common mathematical functions in Visual Basic are Rnd, Sqr, Int, Abs, Exp, Log, Sin, Cos, Tan , Atn, Fix and Round.

(i) Rnd   is very useful when we deal with the concept of chance and probability. The Rnd function returns a random value between 0 and 1. In Example 1. When  you run the program, you will get an output of 10 random numbers between 0 and 1. Randomize Timer is a vital statement here as it will randomize the process.

 Example 1:

          Private Sub Form_Activate

Randomize Timer

For x=1 to 10

Print  Rnd

Next x

End Sub

he Output for example 1 is shown below:    Random numbers in its original form are not very useful in  programming until we convert them to integers. For example, i f we need to obtain a random output of 6 random integers  ranging from 1 to 6, which make the program behave as a  virtual die, we need to convert the random numbers  using the format  Int(Rnd*6)+1. Let’s study the following example: In this example, Int(Rnd*6) will generate a random integer  between 0 and 5 because the function Int truncates the decimal  part of the random number and returns an integer. After adding 1, you will get a random number between 1 and 6 every time  you click the command button. For example, let say the r andom number generated is 0.98, after multiplying it by 6,  it becomes 5.88, and using the integer function Int(5.88)  will convert the number to 5; and after adding 1 you will  get 6.  In this example, you place a command button and  changeits caption to ‘roll die’. You also need to insert a label into the form and clear its caption at the designing phase and make its font bigger and bold. Then set the border value to 1 so that it displays a border; and after that set the alignment to center.  The statement Label1.Caption=Num means the integer generated will be displayed as the caption of the label. Example 2:             Dim num as integer Private Sub Command1_Click ( ) Randomize Timer Num=Int(Rnd*6)+1 Label1.Caption=Num End Sub Now, run the program and then click on the roll die button,  you will get an output like the figure below:   The Numeric Functions     The numeric functions are Int, Sqr, Abs, Exp, Fix, Round and Log. a) Int is the function that converts a number into an integer by truncating its decimal part and the resulting integer is the largest integer that is smaller than the number. For example, Int(2.4)=2, Int(4.8)=4, Int(-4.6)= -5, Int(0.032)=0 and so on. b) Sqr is the function that computes the square root of a number. For example, Sqr(4)=2, Sqr(9)=2 and etc. c) Abs is the function that returns the absolute value of a number.  So Abs(-8) = 8 and Abs(8)= 8. d) Exp of a number x is the value of ex. For example, Exp(1)=e1 = 2.7182818284590 e) Fix and Int are the same if the number is a positive number as both truncate the decimal part of the number and return an integer.  However, when the number is negative, it will return the smallest integer that is larger than the number. For example, Fix(-6.34)= -6 while Int(-6.34)=-7. f) Round is the function that rounds up a number to a certain number of decimal places. The Format is Round (n, m) which means to round a number n to m decimal places. For example, Round (7.2567, 2) =7.26 g) Log is the function that returns the natural Logarithm of a number. For example, Log 10= 2.302585 Example 3 This example computes the values of Int(x), Fix(x)  and Round(x,n) in a table form. It uses the Do Loop statement and the Rnd function to generate 10 numbers.The statement x =  Round (Rnd * 7, 7) rounds a random number between 0 and 7 to  7 decimal places. Using commas in between items will create spaces between them and hence a table of values can be created.  The program  and output are shown below  Private Sub Form_Activate () n = 1 Print " n", "      x", "Int(x)", "Fix(x)", "Round(x, 4)" Do While n < 11 Randomize Timer x = Round (Rnd * 7, 7) Print n, x, Int(x), Fix(x), Round(x, 4) n = n + 1 Loop End Sub