I suspect that the 'Sub Sine()' part might have been a label or text and was not intended to be part of the VBA
Option Explicit only goes one time at the top of a Standard Module
Option Explicit
Sub SinXSeriesExpansion()
Dim M As Long, N As Long, X As Double, SineX As Double
X = InputBox("What is X?")
M = InputBox("How many terms?")
If IsNumeric(M) And M > 0 Then
SineX = 0
On Error GoTo OverFlow
For N = 0 To M \ 1
SineX = SineX + ((-1) ^ (N) * X ^ (2 * N + 1)) / Evaluate("Fact(" & 2 * N + 1 & ")")
Range("A" & N + 1) = SineX
Next
MsgBox SineX
Else
MsgBox "Need the number of terms to be greater than zero!"
End If
Exit Sub
OverFlow:
MsgBox "Too many terms - try fewer terms", , "OverFlow Error!!"
End Sub