Actually, the code you have for Fast_Sin and Fast_Cos runs more slowly than the intrinsic sin and cos functions. This is mainly because of the Mod statement.

If you can insure that the angle never goes beyond +-359 then you can remove that statement. Here is a modified version that runs slightly faster than the intrinsic functions and faster than your original function with more accuracy.
These formulas were derived from the following trig formulas
cos(A+a) = Cos(A)*Cos(a) - Sin(A)*Sin(a)
sin(A+a)= Sin(A)*Cos(a) + Cos(A)*Sin(a)
Sin(a) = a - (a^3)/6 + (a^5)/720 - ... where a is in radians
Cos(a) = 1 - (a^2)/2 + (a^4)/24 - ... where a is in radians
VB Code:
  1. Public Function Fast_Cos(ByVal Theta As Single) As Single

  2.  
  3.     If Theta < 0 Then Theta = Theta + 360

  4.     

  5.     Dim Theta_Integer As Long

  6.     Dim Theta_Fraction As Single

  7.     

  8.     'remove this checking, too slow

  9. '    Theta_Integer = Theta Mod 360

  10.      Theta_Integer = CLng(Theta)

  11.     Theta_Fraction = Theta - Theta_Integer

  12.    

  13.     'Old function

  14.     'Fast_Cos = Cos_Look_Up_Table(Theta_Integer) + Theta_Fraction * (Cos_Look_Up_Table(Theta_Integer + 1) - Cos_Look_Up_Table(Theta_Integer))

  15.     

  16.     'New function

  17.     'cos(A+a) = Cos(A)*Cos(a) - Sin(A)*Sin(a)

  18.     Fast_Cos = Cos_Look_Up_Table(Theta_Integer) - Sin_Look_Up_Table(Theta_Integer) * Theta_Fraction * DegToRad

  19.     

  20. End Function

  21.  
  22. Public Function Fast_Sin(ByVal Theta As Single) As Single

  23.  
  24.     If Theta < 0 Then Theta = Theta + 360

  25.  
  26.     Dim Theta_Integer As Long

  27.     Dim Theta_Fraction As Single

  28.     

  29.     'remove this checking, too slow

  30.     'Theta_Integer = Theta Mod 360

  31.     Theta_Integer = CLng(Theta)

  32.     Theta_Fraction = Theta - Theta_Integer

  33.     'old function

  34.     'Fast_Sin = Sin_Look_Up_Table(Theta_Integer) + Theta_Fraction * (Sin_Look_Up_Table(Theta_Integer + 1) - Sin_Look_Up_Table(Theta_Integer))

  35.  
  36.     'New function

  37.     'sin(A+a)= Sin(A)*Cos(a) + Cos(A)*Sin(a)

  38.     Fast_Sin = Sin_Look_Up_Table(Theta_Integer) + Cos_Look_Up_Table(Theta_Integer) * Theta_Fraction * DegToRad

  39.  
  40. End Function