Sin Function

Returns a Double specifying the sine of an angle.

Syntax

Sin(number)

Parameters

number - Required. Double or any valid numeric expression that expresses an angle in radians.

Return Value

Returns a Double value representing the sine of the angle: - Range: -1 to 1 (inclusive) - Sin(0) = 0 - Sin(π/2) ≈ 1 - Sin(π) ≈ 0 - Sin(3π/2) ≈ -1

Remarks

The Sin function takes an angle in radians and returns the ratio of two sides of a right triangle. The ratio is the length of the side opposite the angle divided by the length of the hypotenuse.

Key characteristics: - Input is in radians, not degrees - To convert degrees to radians: radians = degrees × (π / 180) - To convert radians to degrees: degrees = radians × (180 / π) - π (Pi) ≈ 3.14159265358979 - Use Atn(1) * 4 to calculate π in VB6 - Periodic function: Sin(x) = Sin(x + 2π) - Returns values between -1 and 1

The sine function is one of the fundamental trigonometric functions: - Sin(x): Sine (this function) - Cos(x): Cosine (use Cos function) - Tan(x): Tangent (use Tan function or Sin(x)/Cos(x))

Common angles and their sines: - Sin(0°) = Sin(0 rad) = 0 - Sin(30°) = Sin(π/6 rad) = 0.5 - Sin(45°) = Sin(π/4 rad) ≈ 0.707 - Sin(60°) = Sin(π/3 rad) ≈ 0.866 - Sin(90°) = Sin(π/2 rad) = 1 - Sin(180°) = Sin(π rad) = 0 - Sin(270°) = Sin(3π/2 rad) = -1 - Sin(360°) = Sin(2π rad) = 0

Typical Uses

Wave Generation: Create sine waves for animations or signals
Circular Motion: Calculate vertical position in circular paths
Oscillations: Model periodic oscillating systems
Physics Simulations: Projectile motion, pendulum swing
Graphics: Rotation, transformation, curve drawing
Audio Processing: Sine wave tone generation
Engineering Calculations: Structural analysis, AC circuits
Game Development: Movement patterns, trajectories

Basic Examples

' Example 1: Calculate sine of 45 degrees
Const PI As Double = 3.14159265358979
Dim angle45 As Double
Dim sineValue As Double

angle45 = 45 * (PI / 180)  ' Convert to radians
sineValue = Sin(angle45)   ' Returns ≈ 0.707

' Example 2: Calculate sine of π/2 (90 degrees)
Const PI As Double = 3.14159265358979
Dim result As Double
result = Sin(PI / 2)  ' Returns 1

' Example 3: Use with Atn to calculate π
Dim pi As Double
Dim sineValue As Double
pi = Atn(1) * 4
sineValue = Sin(pi)  ' Returns ≈ 0 (very small number)

' Example 4: Sine wave generation
Dim i As Integer
Dim y As Double
For i = 0 To 360
y = Sin(i * (Atn(1) * 4) / 180)
Debug.Print i & " degrees: " & y
Next i

Common Patterns

Pattern 1: `DegreesToRadians`

Convert degrees to radians for Sin function

Function DegreesToRadians(degrees As Double) As Double
Const PI As Double = 3.14159265358979
DegreesToRadians = degrees * (PI / 180)
End Function

' Usage:
result = Sin(DegreesToRadians(45))

Pattern 2: `SinDegrees`

Sine function that accepts degrees

Function SinDegrees(degrees As Double) As Double
Const PI As Double = 3.14159265358979
SinDegrees = Sin(degrees * (PI / 180))
End Function

Pattern 3: `GenerateSineWave`

Generate array of sine wave values

Function GenerateSineWave(samples As Integer, amplitude As Double, _
frequency As Double) As Double()
Dim result() As Double
Dim i As Integer
Dim angle As Double
Const PI As Double = 3.14159265358979

ReDim result(0 To samples - 1)

For i = 0 To samples - 1
angle = (i / samples) * 2 * PI * frequency
result(i) = amplitude * Sin(angle)
Next i

GenerateSineWave = result
End Function

Pattern 4: `CircularMotionY`

Calculate vertical position in circular motion

Function CircularMotionY(centerY As Double, radius As Double, _
angle As Double) As Double
' angle in radians
CircularMotionY = centerY + radius * Sin(angle)
End Function

Pattern 5: `OscillatingValue`

Create oscillating value over time

Function OscillatingValue(time As Double, amplitude As Double, _
frequency As Double, Optional phase As Double = 0) As Double
Const PI As Double = 3.14159265358979
OscillatingValue = amplitude * Sin(2 * PI * frequency * time + phase)
End Function

Pattern 6: `SineInterpolation`

Smooth interpolation using sine

Function SineInterpolation(startValue As Double, endValue As Double, _
t As Double) As Double
' t ranges from 0 to 1
Dim factor As Double
Const PI As Double = 3.14159265358979

factor = (1 - Cos(t * PI)) / 2
SineInterpolation = startValue + (endValue - startValue) * factor
End Function

Pattern 7: `AngleFromSine`

Get angle from sine value (inverse sine approximation)

Function ArcSineApprox(sineValue As Double) As Double
' For small angles, asin(x) ≈ x
' For better accuracy, use iterative methods or Atn
' Using Atn for proper arcsin:
If Abs(sineValue) >= 1 Then
ArcSineApprox = Sgn(sineValue) * Atn(1) * 2
Else
ArcSineApprox = Atn(sineValue / Sqr(1 - sineValue * sineValue))
End If
End Function

Pattern 8: `SineWaveAnalysis`

Analyze sine wave properties

Sub AnalyzeSineWave(amplitude As Double, frequency As Double, _
ByRef maxVal As Double, ByRef minVal As Double, _
ByRef period As Double)
Const PI As Double = 3.14159265358979

maxVal = amplitude
minVal = -amplitude
period = 1 / frequency  ' In seconds or time units
End Sub

Pattern 9: `ProjectileMotionY`

Calculate vertical position in projectile motion

Function ProjectileY(initialY As Double, velocity As Double, _
angle As Double, time As Double, gravity As Double) As Double
' angle in radians
Dim verticalVelocity As Double

verticalVelocity = velocity * Sin(angle)
ProjectileY = initialY + verticalVelocity * time - 0.5 * gravity * time * time
End Function

Pattern 10: `HarmonicMotion`

Simple harmonic motion displacement

Function HarmonicDisplacement(amplitude As Double, angularFrequency As Double, _
time As Double, Optional phase As Double = 0) As Double
HarmonicDisplacement = amplitude * Sin(angularFrequency * time + phase)
End Function

Advanced Usage

Example 1: `WaveformGenerator` Class

Generate various waveforms using sine function

' Class: WaveformGenerator
Private Const PI As Double = 3.14159265358979
Private m_sampleRate As Long
Private m_duration As Double

Public Sub Initialize(sampleRate As Long, duration As Double)
m_sampleRate = sampleRate
m_duration = duration
End Sub

Public Function GenerateSineWave(frequency As Double, amplitude As Double) As Double()
Dim samples As Long
Dim result() As Double
Dim i As Long
Dim t As Double

samples = CLng(m_sampleRate * m_duration)
ReDim result(0 To samples - 1)

For i = 0 To samples - 1
t = i / m_sampleRate
result(i) = amplitude * Sin(2 * PI * frequency * t)
Next i

GenerateSineWave = result
End Function

Public Function GenerateAMWave(carrier As Double, modulator As Double, _
amplitude As Double, modDepth As Double) As Double()
' Amplitude Modulation
Dim samples As Long
Dim result() As Double
Dim i As Long
Dim t As Double
Dim envelope As Double

samples = CLng(m_sampleRate * m_duration)
ReDim result(0 To samples - 1)

For i = 0 To samples - 1
t = i / m_sampleRate
envelope = 1 + modDepth * Sin(2 * PI * modulator * t)
result(i) = amplitude * envelope * Sin(2 * PI * carrier * t)
Next i

GenerateAMWave = result
End Function

Public Function GenerateFMWave(carrier As Double, modulator As Double, _
amplitude As Double, modIndex As Double) As Double()
' Frequency Modulation
Dim samples As Long
Dim result() As Double
Dim i As Long
Dim t As Double
Dim phase As Double

samples = CLng(m_sampleRate * m_duration)
ReDim result(0 To samples - 1)

For i = 0 To samples - 1
t = i / m_sampleRate
phase = 2 * PI * carrier * t + modIndex * Sin(2 * PI * modulator * t)
result(i) = amplitude * Sin(phase)
Next i

GenerateFMWave = result
End Function

Public Function GenerateHarmonics(fundamental As Double, harmonics As Integer, _
amplitude As Double) As Double()
' Generate complex tone with harmonics
Dim samples As Long
Dim result() As Double
Dim i As Long
Dim h As Integer
Dim t As Double
Dim value As Double

samples = CLng(m_sampleRate * m_duration)
ReDim result(0 To samples - 1)

For i = 0 To samples - 1
t = i / m_sampleRate
value = 0

For h = 1 To harmonics
value = value + (amplitude / h) * Sin(2 * PI * fundamental * h * t)
Next h

result(i) = value
Next i

GenerateHarmonics = result
End Function

Example 2: `CircularMotion` Module

Calculate circular and elliptical motion using trigonometry

' Module: CircularMotion
Private Const PI As Double = 3.14159265358979

Public Sub GetCircularPosition(centerX As Double, centerY As Double, _
radius As Double, angle As Double, _
ByRef x As Double, ByRef y As Double)
' angle in radians
x = centerX + radius * Cos(angle)
y = centerY + radius * Sin(angle)
End Sub

Public Sub GetEllipticalPosition(centerX As Double, centerY As Double, _
radiusX As Double, radiusY As Double, _
angle As Double, ByRef x As Double, ByRef y As Double)
' angle in radians
x = centerX + radiusX * Cos(angle)
y = centerY + radiusY * Sin(angle)
End Sub

Public Function CalculateAngularVelocity(rpm As Double) As Double
' Convert revolutions per minute to radians per second
CalculateAngularVelocity = (rpm / 60) * 2 * PI
End Function

Public Sub AnimateCircularMotion(centerX As Double, centerY As Double, _
radius As Double, angularVelocity As Double, _
time As Double, ByRef x As Double, ByRef y As Double)
Dim angle As Double
angle = angularVelocity * time

x = centerX + radius * Cos(angle)
y = centerY + radius * Sin(angle)
End Sub

Public Function CalculateTangentialVelocity(radius As Double, _
angularVelocity As Double) As Double
' v = r * ω
CalculateTangentialVelocity = radius * angularVelocity
End Function

Public Sub GetVelocityComponents(speed As Double, angle As Double, _
ByRef vx As Double, ByRef vy As Double)
' angle in radians from horizontal
vx = speed * Cos(angle)
vy = speed * Sin(angle)
End Sub

Example 3: `PhysicsSimulator` Class

Simulate physics using trigonometric functions

' Class: PhysicsSimulator
Private Const PI As Double = 3.14159265358979
Private Const GRAVITY As Double = 9.81  ' m/s²

Public Function CalculateRange(velocity As Double, angle As Double) As Double
' Projectile range formula: R = v² * sin(2θ) / g
' angle in radians
CalculateRange = (velocity * velocity * Sin(2 * angle)) / GRAVITY
End Function

Public Function CalculateMaxHeight(velocity As Double, angle As Double) As Double
' Max height: H = (v * sin(θ))² / (2g)
Dim verticalVelocity As Double
verticalVelocity = velocity * Sin(angle)
CalculateMaxHeight = (verticalVelocity * verticalVelocity) / (2 * GRAVITY)
End Function

Public Function CalculateTimeOfFlight(velocity As Double, angle As Double) As Double
' Time of flight: T = 2 * v * sin(θ) / g
CalculateTimeOfFlight = (2 * velocity * Sin(angle)) / GRAVITY
End Function

Public Sub GetProjectilePosition(velocity As Double, angle As Double, _
time As Double, ByRef x As Double, ByRef y As Double)
' angle in radians
Dim vx As Double, vy As Double

vx = velocity * Cos(angle)
vy = velocity * Sin(angle)

x = vx * time
y = vy * time - 0.5 * GRAVITY * time * time
End Sub

Public Function CalculatePendulumDisplacement(length As Double, angle0 As Double, _
time As Double) As Double
' Small angle approximation
' angle(t) = angle0 * cos(ωt) where ω = sqrt(g/L)
Dim omega As Double
omega = Sqr(GRAVITY / length)

' For small angles, displacement ≈ L * θ
CalculatePendulumDisplacement = length * angle0 * Cos(omega * time)
End Function

Public Function CalculateInclinedPlaneForce(mass As Double, angle As Double) As Double
' Force down incline: F = m * g * sin(θ)
' angle in radians
CalculateInclinedPlaneForce = mass * GRAVITY * Sin(angle)
End Function

Example 4: `GraphicsHelper` Module

Graphics and animation helpers using trigonometry

' Module: GraphicsHelper
Private Const PI As Double = 3.14159265358979

Public Function RotatePointX(x As Double, y As Double, angle As Double, _
centerX As Double, centerY As Double) As Double
' Rotate point around center, return new X
' angle in radians
Dim dx As Double, dy As Double

dx = x - centerX
dy = y - centerY

RotatePointX = centerX + dx * Cos(angle) - dy * Sin(angle)
End Function

Public Function RotatePointY(x As Double, y As Double, angle As Double, _
centerX As Double, centerY As Double) As Double
' Rotate point around center, return new Y
' angle in radians
Dim dx As Double, dy As Double

dx = x - centerX
dy = y - centerY

RotatePointY = centerY + dx * Sin(angle) + dy * Cos(angle)
End Function

Public Function CreatePulseEffect(time As Double, frequency As Double) As Double
' Create pulsing effect (0 to 1)
CreatePulseEffect = (Sin(2 * PI * frequency * time) + 1) / 2
End Function

Public Function CreateFadeInOut(time As Double, duration As Double) As Double
' Smooth fade in and out using sine
Dim t As Double
t = (time / duration) * PI
CreateFadeInOut = Sin(t)
End Function

Public Function EaseInOutSine(t As Double) As Double
' Easing function using sine (t from 0 to 1)
EaseInOutSine = -(Cos(PI * t) - 1) / 2
End Function

Public Sub DrawSineWave(picBox As Object, amplitude As Double, _
frequency As Double, Optional phase As Double = 0)
Dim x As Integer
Dim y As Double
Dim prevX As Integer, prevY As Integer
Dim width As Integer

width = picBox.ScaleWidth

For x = 0 To width
y = amplitude * Sin(2 * PI * frequency * (x / width) + phase)
y = picBox.ScaleHeight / 2 - y  ' Flip Y axis

If x > 0 Then
picBox.Line (prevX, prevY)-(x, y)
End If

prevX = x
prevY = y
Next x
End Sub

Error Handling

The Sin function can generate the following errors:

Error 13 (Type mismatch): Argument cannot be interpreted as numeric
Error 5 (Invalid procedure call): In rare cases with invalid input

Error handling example:

On Error Resume Next
result = Sin(angle)
If Err.Number <> 0 Then
MsgBox "Error calculating sine: " & Err.Description
End If

Performance Considerations

Sin is a relatively fast mathematical function
Uses hardware FPU for calculation when available
For repeated calculations with same angles, consider caching results
Lookup tables can be faster for real-time applications with limited angle sets
Modern CPUs execute Sin very quickly (microseconds)

Best Practices

Use Radians: Remember Sin takes radians, not degrees
Convert Carefully: Use consistent conversion factor for degrees↔radians
Cache Pi: Define PI as a constant rather than calculating repeatedly
Range Awareness: Sin always returns -1 to 1
Precision: Be aware of floating-point precision limits
Angle Normalization: For large angles, consider normalizing to 0-2π
Avoid Division: Use multiplication by inverse when possible
Test Edge Cases: Test with 0, π/2, π, 3π/2, 2π
Document Units: Always document whether angles are in degrees or radians
Combine Functions: Use with Cos, Tan for complete trigonometric operations

Function	Input (radians)	Output Range	Description
Sin	angle	-1 to 1	Sine of angle
Cos	angle	-1 to 1	Cosine of angle
Tan	angle	-∞ to +∞	Tangent of angle
Atn	ratio	-π/2 to π/2	Arctangent (inverse tangent)
Sqr	number ≥ 0	≥ 0	Square root

Platform Considerations

Available in VB6, VBA (all versions)
Uses system math library
Precision depends on Double data type (IEEE 754)
Results consistent across Windows versions
Very small return values near multiples of π due to floating-point precision

Limitations

Input must be in radians (no built-in degree support)
Floating-point precision limits (≈15-17 decimal digits)
Sin(π) returns very small number, not exactly 0
Large angle values may accumulate rounding errors
No complex number support
No automatic angle normalization

Cos: Returns the cosine of an angle in radians
Tan: Returns the tangent of an angle in radians
Atn: Returns the arctangent of a number in radians
Sqr: Returns the square root (used in inverse sine calculations)
Abs: Returns absolute value (useful for angle normalization)

Sin Function

Syntax

Parameters

Return Value

Remarks

Typical Uses

Basic Examples

Common Patterns

Pattern 1: DegreesToRadians

Pattern 2: SinDegrees

Pattern 3: GenerateSineWave

Pattern 4: CircularMotionY

Pattern 5: OscillatingValue

Pattern 6: SineInterpolation

Pattern 7: AngleFromSine

Pattern 8: SineWaveAnalysis

Pattern 9: ProjectileMotionY

Pattern 10: HarmonicMotion