Atn Function

Returns a Double specifying the arctangent of a number.

Syntax

Atn(number)

Parameters

• number - Required. A Double or any valid numeric expression. The tangent value for which you want the angle.

Return Value

Returns a Double representing the arctangent of the number in radians.

• The result is in the range -π/2 to π/2 radians (-90° to 90°)
• To convert from radians to degrees, multiply by 180/π (approximately 57.2957795130823)
• To convert from degrees to radians, multiply by π/180 (approximately 0.0174532925199433)

Remarks

The Atn function takes the ratio of two sides of a right triangle (opposite/adjacent) and returns the corresponding angle in radians. This is the inverse of the tangent function.

Important Notes

1. Return Type: Always returns Double regardless of input type
2. Radians: Result is always in radians, not degrees
3. Range: Return value is between -π/2 and π/2 (-1.5708 to 1.5708 radians)
4. Ratio Input: The argument represents the tangent (opposite/adjacent) of the angle
5. Inverse Function: Atn is the inverse of Tan (Atn(Tan(x)) = x for x in valid range)

Mathematical Relationship

' For a right triangle:
angle = Atn(opposite / adjacent)

' Converting between functions:
Tan(Atn(x)) = x    ' Always true
Atn(Tan(x)) = x    ' True when -π/2 < x < π/2

Special Values

• Atn(0) returns 0 (angle is 0 radians or 0°)
• Atn(1) returns π/4 (approximately 0.785398, which is 45°)
• Atn(-1) returns -π/4 (approximately -0.785398, which is -45°)
• Large positive values approach π/2 (90°)
• Large negative values approach -π/2 (-90°)

Examples

Basic Usage

Dim angle As Double
angle = Atn(1)              ' Returns π/4 (approx 0.785398) = 45°
angle = Atn(0)              ' Returns 0 = 0°
angle = Atn(-1)             ' Returns -π/4 (approx -0.785398) = -45°
angle = Atn(1.732050808)    ' Returns π/3 (approx 1.047198) = 60°

Converting to Degrees

Function AtnDegrees(tangent As Double) As Double
Const PI As Double = 3.14159265358979
AtnDegrees = Atn(tangent) * 180 / PI
End Function

' Usage:
angle = AtnDegrees(1)       ' Returns 45 degrees

Calculating Angle from Triangle Sides

Function AngleFromSides(opposite As Double, adjacent As Double) As Double
' Returns angle in radians
AngleFromSides = Atn(opposite / adjacent)
End Function

' For a right triangle with opposite=3, adjacent=4:
angle = AngleFromSides(3, 4)    ' Returns angle in radians

Calculating π

Function CalculatePi() As Double
' Since Atn(1) = π/4, then 4 * Atn(1) = π
CalculatePi = 4 * Atn(1)
End Function

Full Circle Angle Calculation (Atn2 Emulation)

Function Atn2(y As Double, x As Double) As Double
' Emulates atan2 function for full circle (-π to π)
Const PI As Double = 3.14159265358979

If x > 0 Then
Atn2 = Atn(y / x)
ElseIf x < 0 Then
If y >= 0 Then
Atn2 = Atn(y / x) + PI
Else
Atn2 = Atn(y / x) - PI
End If
ElseIf y > 0 Then
Atn2 = PI / 2
ElseIf y < 0 Then
Atn2 = -PI / 2
Else
Atn2 = 0  ' Undefined, but return 0
End If
End Function

Common Patterns

1. Slope to Angle Conversion

Dim slope As Double
Dim angleRadians As Double
Dim angleDegrees As Double

slope = 0.5  ' Rise over run
angleRadians = Atn(slope)
angleDegrees = angleRadians * 180 / (4 * Atn(1))

2. Direction Calculation

Function GetDirection(deltaX As Double, deltaY As Double) As Double
' Returns angle in degrees (0-360)
Const PI As Double = 3.14159265358979
Dim angle As Double

If deltaX = 0 Then
If deltaY > 0 Then
angle = 90
ElseIf deltaY < 0 Then
angle = 270
Else
angle = 0
End If
Else
angle = Atn(deltaY / deltaX) * 180 / PI
If deltaX < 0 Then angle = angle + 180
If angle < 0 Then angle = angle + 360
End If

GetDirection = angle
End Function

3. Distance and Angle from Origin

Sub GetPolarCoordinates(x As Double, y As Double, _
distance As Double, angle As Double)
distance = Sqr(x * x + y * y)

If x = 0 Then
If y > 0 Then
angle = 90
Else
angle = 270
End If
Else
angle = Atn(y / x) * 180 / (4 * Atn(1))
If x < 0 Then angle = angle + 180
End If
End Sub

4. Graphics Rotation

Function RotatePoint(x As Double, y As Double, _
centerX As Double, centerY As Double, _
angleDegrees As Double)
Const PI As Double = 3.14159265358979
Dim angleRadians As Double
Dim currentAngle As Double
Dim distance As Double
Dim newAngle As Double

' Get current angle and distance from center
distance = Sqr((x - centerX) ^ 2 + (y - centerY) ^ 2)
currentAngle = Atn((y - centerY) / (x - centerX))

' Calculate new angle
angleRadians = angleDegrees * PI / 180
newAngle = currentAngle + angleRadians

' Calculate new position
x = centerX + distance * Cos(newAngle)
y = centerY + distance * Sin(newAngle)
End Function

5. Navigation Bearing

Function CalculateBearing(lat1 As Double, lon1 As Double, _
lat2 As Double, lon2 As Double) As Double
Const PI As Double = 3.14159265358979
Dim dLon As Double
Dim y As Double
Dim x As Double
Dim bearing As Double

dLon = lon2 - lon1
y = Sin(dLon) * Cos(lat2)
x = Cos(lat1) * Sin(lat2) - Sin(lat1) * Cos(lat2) * Cos(dLon)
bearing = Atn(y / x) * 180 / PI

' Normalize to 0-360
CalculateBearing = (bearing + 360) Mod 360
End Function

6. Inverse Trigonometry Relationships

' Calculate arcsine using Atn
Function Asin(x As Double) As Double
Asin = Atn(x / Sqr(1 - x * x))
End Function

' Calculate arccosine using Atn
Function Acos(x As Double) As Double
Const PI As Double = 3.14159265358979
Acos = PI / 2 - Atn(x / Sqr(1 - x * x))
End Function

7. Tangent Line Slope

Function GetTangentAngle(x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
Dim slope As Double
Const PI As Double = 3.14159265358979

If x2 = x1 Then
GetTangentAngle = 90  ' Vertical line
Else
slope = (y2 - y1) / (x2 - x1)
GetTangentAngle = Atn(slope) * 180 / PI
End If
End Function

8. Game Development - Projectile Angle

Function AimAngle(shooterX As Double, shooterY As Double, _
targetX As Double, targetY As Double) As Double
Const PI As Double = 3.14159265358979
Dim deltaX As Double
Dim deltaY As Double

deltaX = targetX - shooterX
deltaY = targetY - shooterY

If deltaX = 0 Then
If deltaY > 0 Then
AimAngle = 90
Else
AimAngle = 270
End If
Else
AimAngle = Atn(deltaY / deltaX) * 180 / PI
If deltaX < 0 Then AimAngle = AimAngle + 180
If AimAngle < 0 Then AimAngle = AimAngle + 360
End If
End Function

Common Trigonometric Values

Type Conversion

Error Conditions

• Type Mismatch: If the argument cannot be converted to a numeric value
• No overflow: Unlike some functions, Atn cannot overflow as it's bounded to ±π/2

Related Functions

• Tan: Returns the tangent of an angle (inverse of Atn)
• Sin: Returns the sine of an angle
• Cos: Returns the cosine of an angle
• Sqr: Returns the square root (used with Atn to calculate other inverse trig functions)
• Abs: Returns absolute value (useful in angle calculations)

Performance Notes

• Atn is a fast intrinsic function
• Implemented using CPU floating-point instructions
• No significant performance difference between Integer, Long, or Double arguments
• For repeated π calculations, cache the value of 4 * Atn(1) rather than recalculating

Parsing Notes

The Atn function is not a reserved keyword in VB6. It is parsed as a regular function call (CallExpression). This module exists primarily for documentation purposes and to provide a comprehensive test suite that validates the parser correctly handles Atn function calls in various contexts.