Sin Function

Hi all,

If you have ever wondered how the sin function works then this function should explain nicely.

It uses some standard reduction formulas and a Taylor series approximation of the sin function of 4 terms.(if you had highschool math this should make sense)
The difference between this function and Math.sin is usually smaller than 0.0000001

The sin Function is where the reduction formulas are contained and the sin_ex is where the taylor series approximation is. You can add more terms to make it more accurate but the difference will be extremely small.

vb.net Code:

Const pi As Double = 3.1415926535897931
    Function Sin(ByVal x As Double) As Double 'valid for x > 0
        x = x Mod (2 * pi)
        If x < (pi / 2) And x > -(pi / 2) Then
            Return Sin_ex(x)
        Else
            Return Sin_ex(pi - x)
        End If
    End Function
 
    Function Sin_ex(ByVal x As Double) As Double 'Valid for [-pi/2;pi/2]
        Return x - ((x ^ 3) / 6) + ((x ^ 5) / 120) - ((x ^ 7) / 5040) '+ ((x ^ 9) / 326880) 
    End Function

Some notes:

• Only for positive values
• It's in radians
• For some reason the approximation gets inaccurate for values between multiples of pi/2 and pi.(about accurate to the second decimal)
• this was compared to the Math.Sin Function. I assumed in was 100% correct

EDIT: If you want Cos, there is a Taylor series approximation for that as well, but you can implement cos using sin quite easily since cos(x) = sin(x+pi/2) . And if you have cos then tan is quite easy aswell since tan(x) = sin(x)/cos(x)

Just so you know...the framework has Math.PI built in.

I know, when I made the function I didn't want any dependency on the Math module, but then I ended up using math.truncate

I discovered that you can actually use mod on floating point numbers. Now I don't need that ugly first if statement.

Quote:

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Originally Posted by BlindSniper

I know, when I made the function I didn't want any dependency on the Math module, but then I ended up using math.truncate

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Ahh gotcha.