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	Measure-Based Functions: The Pi Constant

 

The letter п, also written as Pi, is a constant number used in various mathematical calculations. Its approximate value is 3.1415926535897932. The calculator of Windows represents it as 3.1415926535897932384626433832795. Borland had included its value in the math.h library as M_PI 3.14159265358979323846.

A diameter is two times the radius. In geometry, it is written as 2R. In C++, it is written as 2 * R or R * 2 (because the multiplication is symmetric). The circumference of a circle is calculated by multiplying the diameter to Pi, which is 2Rп, or 2 * R * п or 2 * R * Pi.

A radian is 2Rп/R radians or 2Rп/R rad, which is the same as 2п rad or 2 * Pi rad.

To perform conversions between the degree and the radian, you can use the formula:

360˚ = 2п rad which is equivalent to 1 rad = 360˚ / 2п = 57.3˚ 

	Measure-Based Functions: Cycle To Radius Conversion

 

Extended __fastcall CycleToRad(Extended Cycles);

The CycleToRad() function is used to convert the measurement of an angle from radians to cycles. This function is equivalent to using the formula Radian = 2Pi * Cycle Here is an example:

//---------------------------------------------------------------------------
#include <MATH.HPP>
#include <vcl.h>

#pragma hdrstop
#include "Unit1.h"
//---------------------------------------------------------------------------

#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner)
 : TForm(Owner)
{

}
//---------------------------------------------------------------------------
void __fastcall TForm1::btnConversionClick(TObject *Sender)
{
 Extended Cyc = StrToFloat(edtCycle->Text);
 Extended Rad = CycleToRad(Cyc);
 
 edtRadian->Text = FloatToStr(Rad);
}
//---------------------------------------------------------------------------

 

	Measure-Based Functions: Degrees To Radius Conversion

 

Extended __fastcall DegToRad(Extended Degrees);

The DegToRad() function is used to calculate the equivalent value of an angle from degrees to radians. This function follows the formula:

2Pi rad = 360˚

which is

1 rad = 360˚ / 2Pi = 180˚ / Pi = 57.3˚

Here is an example:

//---------------------------------------------------------------------------
void __fastcall TForm1::btnConversionClick(TObject *Sender)
{
 Extended Deg = StrToFloat(edtDegrees->Text);
 Extended Rad = DegToRad(Deg);
 
 edtRadians->Text = FloatToStr(Rad);
}
//---------------------------------------------------------------------------

 

	Measure-Based Functions: Radius To Cycle Conversion

 

Extended __fastcall RadToCycle(Extended Radians);

The RadToCycle() function is used to convert the measurement of an angle from radians to cycles. This function is equivalent to using the formula

Cycle = Radian / 2Pi

Here is an example:

//---------------------------------------------------------------------------
void __fastcall TForm1::btnConversionClick(TObject *Sender)
{
 Extended Rad = StrToFloat(edtRadian->Text);
 Extended Cyc = RadToCycle(Rad);
 
 edtCycle->Text = FloatToStr(Cyc);
}
//---------------------------------------------------------------------------

	Measure-Based Functions: Radius To Degrees Conversion

  

Extended __fastcall RadToDeg(Extended Radians);

The RadToDeg() function is used to calculate the equivalent value of an angle from radians to degrees. This function applies the formula:

360˚ = 2 * Pi

which is

1˚ = 2 * Pi

Here is an example:

//---------------------------------------------------------------------------
void __fastcall TForm1::btnConversionClick(TObject *Sender)
{
 Extended Rad = StrToFloat(edtRadians->Text);
 Extended Deg = RadToDeg(Rad);
 
 edtDegrees->Text = FloatToStr(Deg);
}
//---------------------------------------------------------------------------