Trigonometric values to 30 DP?

[Monkfish]

I need to calculate cos of very small angles (~10^-10 radians) very accurately (30 decimal places).

I obviously need some way to implement the trigonometric expansion of cos to many decimal places. How can this be done using a computer algorithm if the computer is only accurate to 7 significant figures?

I suppose it's like working out pi to millions of digits.

[VBAhack]

Welcome to the forums!

One way is to have numbers represented by strings and write special routines. The Foxes group (Italy) has an incredible Excel add-in called Xnumbers that performs variable precision calculations up to 200 digits. Their documentation is outstanding. They recently added a DLL version that allows you to call the routines from VB/VBA. Best part - freeware!

http://digilander.libero.it/foxes/SoftwareDownload.htm

[Monkfish]

Thanks VBA, I'll take a look.

[VBAhack]

Here's an example using the DLL:

Sub TestXnumbers()
    Dim x1 As Xnumbers, x As Double
    Set x1 = New Xnumbers
    
    x = 0.0000000001
    Debug.Print Cos(x)
    Debug.Print x1.xCos(x, 30)
    Debug.Print x1.xCos(x, 45)
    Debug.Print x1.xCos(x, 55)
    Debug.Print x1.xCos(x, 65)
    '1
    '0.999999999999999999995
    '0.999999999999999999995000000000000000000004166
    '0.9999999999999999999950000000000000000000041666666666666
    '0.99999999999999999999500000000000000000000416666666666666666666527
End Sub