Trigonometric Functions:
The Cosine of a Value

double cos(double x);
long double cosl(long double x);

The cos() function calculates the cosine of a number.

Consider AB the length of A to B, also referred to as the hypotenuse. Also consider AC the length of A to C which is the side adjacent to point A. The cosine of the angle at point A is the ratio AC/AB. That is, the ratio of the adjacent length, AC, over the length of the hypotenuse, AB:

The returned value, the ratio, is a double-precision number between –1 and 1.

Example: A form contains an Edit control named edtValue. After the user has typed a value and presses Enter, the OnKeyPress event retrieves the number typed in the edit box, calculates its cosine and displays it in the same Edit control:

//---------------------------------------------------------------------------
void __fastcall TForm1::edtValueKeyPress(TObject *Sender, char &Key)
{
	if( Key == VK_RETURN )
	{
		double Value = edtValue->Text.ToDouble();
		double Cosinus = cos(Value);
		
		edtValue->Text = Cosinus;
	}
}
//---------------------------------------------------------------------------

double sin(double x);
long double sinl(long double x);

The sin() function calculates the sine of a number.

Consider AB the length of A to B, also called the hypotenuse to point A. Also consider CB the length of C to B, which is the opposite side to point A. The sine represents the ratio of CB/AB; that is, the ratio of the opposite side, CB over the hypotenuse AB.

The sin() function takes a double-precision number and returns one between –1 and 1. The sinl() function is used for 10-byte values.

Example: A form contains an Edit control named edtValue. After the user has typed a value and presses Enter, the OnKeyPress event retrieves the number typed in the edit box, calculates its sine and displays the result in the same Edit control:

//---------------------------------------------------------------------------
void __fastcall TForm1::edtValueKeyPress(TObject *Sender, char &Key)
{
	if( Key == VK_RETURN )
	{
		double Value = edtValue->Text.ToDouble();
		double Sinus = sin(Value);
		
		edtValue->Text = Sinus;
	}
}
//---------------------------------------------------------------------------

double tan(double x);
long double tanl(long double x);

The tan() function calculates the tangent of a number.

In geometry, consider AC the length of A to C. Also consider BC the length of B to C. The tangent is the result of BC/AB; that is, the ratio of BC over AB.

Example: A form contains an Edit control named edtValue. After the user has typed a value and presses Enter, the OnKeyPress event retrieves the number typed in the edit box, calculates its tangent and displays the result in the same Edit control:

//---------------------------------------------------------------------------
void __fastcall TForm1::edtValueKeyPress(TObject *Sender, char &Key)
{
	if( Key == VK_RETURN )
	{
		double Value = edtValue->Text.ToDouble();
		double Tangent = tan(Value);
		
		edtValue->Text = Tangent;
	}
}
//---------------------------------------------------------------------------

double atan(double x);

The atan() function is used to calculate the arc tangent of a number.

In geometry, consider BC the length of B to C. Also consider AC the length of A to C. The arc tangent is the ratio of BC/AC.

The atan() function takes one argument, x, that represents the angle BA AC. After the evaluation, the function returns a double-precision number between –PI/2 and PI/2.

If the number to be evaluated is larger than a double, use the atanl() function:

long double atanl(long double x);

This function takes a long double argument and returns a long double.