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PROCEDURES
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Fig. 7.13 A function reference may appear within a more complex expression, as though the function name were an ordinary variable. However, any required arguments must follow the function name, enclosed in parentheses and separated by commas.
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EXAMPLE 7.7 CALCULATING THE SINE OF AN ANGLE
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In trigonometry, the sine of an angle within a right triangle is the value obtained when the side opposite the angle is divided by the hypoteneuse. Thus, in Fig. 7.14, the sine of the angle x is the quotient a/c. This quantity, usually written as sin(x), is used in numerous scientific and technical applications, many of which do not involve geometry. (Note that the angle x is expressed in radians, where 2 radians = 360 .)
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c a x b
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Fig. 7.14
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The numerical value of sin(x) can easily be determined using the Visual Basic sin function, provided x (in radians) is given as an argument. However, the value of sin(x) can also be approximated by the series sin(x) = x x3 x5 x7 + + 3! 5! 7! =
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i =1
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( 1) (i +1) ( 2i 1)!
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x 2 i 1
The accuracy of this approximation increases as the number of terms in the series (n) increases. In principle, the summation results in an exact answer when n becomes infinite. As a practical matter, the summation is usually sufficiently accurate for modestly large values of n (say, n = 5 or n = 6).
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PROCEDURES
In this example we will develop a Visual Basic program that evaluates sin(x) using the first n terms of the series expansion, and then compares this value with the more accurate value returned from the Visual Basic sin function. The values of x (in degrees) and n will be input values. When evaluating the series expansion, we will make use of the Factorial function procedure presented in the last two examples. The preliminary control layout is shown in Fig. 7.15, followed by the initial property assignments.
Object Form1 Label1 Label2 Label3 Label4 Label5 Label6 Text1 Text2 Text3 Property Caption Caption Font Caption Font Caption Font Caption Font Caption Font Caption Font Caption Font Caption Font Caption Font (Continues on next page)
AM FL Y
Fig. 7.15
Value Sine of x Series approximation for sin(x) MS Sans Serif, 12-point x = MS Sans Serif, 10-point n = MS Sans Serif, 10-point Sin (x): MS Sans Serif, 10-point Series approximation: MS Sans Serif, 10-point Correct value: MS Sans Serif, 10-point (none) MS Sans Serif, 10-point (none) MS Sans Serif, 10-point (none) MS Sans Serif, 10-point
Team-Fly
PROCEDURES
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Object Text4 Command1 Command2 Command3
Property Caption Font Caption Font Caption Font Caption Font
Value (none) MS Sans Serif, 10-point Go MS Sans Serif, 10-point Clear MS Sans Serif, 10-point Quit MS Sans Serif, 10-point
These assignments result in the final Form Design Window shown in Fig. 7.16.
Fig. 7.16
The required procedures are shown below. Notice that the first procedure is the function procedure Factorial, which is repeated from the previous two examples. Also, note that Factorial is accessed as a part of an expression within the event procedure Command1_Click.
Function Factorial(n As Integer) As Long Dim i As Integer If n < 1 Then Beep MsgBox ("ERROR - Please try again") Else Factorial = 1 For i = 1 To n Factorial = Factorial * i Next i End If End Function
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PROCEDURES
Private Sub Command1_Click() Const Pi As Single = 3.1415927 Dim n As Integer, i As Integer Dim Angle As Single, Rad As Single, Approx As Single, Exact As Single Dim Sum As Single, C As Single Angle = Val(Text1.Text) Rad = 2 * Pi * Angle / 360 n = Val(Text2.Text)
'convert angle to radians
Sum = 0 C = 1 For i = 1 To n Sum = Sum + C * Rad ^ (2 * i - 1) / Factorial(2 * i - 1) C = -C 'reverse sign for next member in series Next i Approx = Sum Exact = Sin(Rad) 'library function Text3.Text = Str(Approx) Text4.Text = Str(Exact) End Sub Private Sub Command2_Click() Text1.Text = "" Text2.Text = "" Text3.Text = "" Text4.Text = ""
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