alignment – Align 1st row of Grid different from the other rows

The grid formed below aligns its columns as I want on the decimal point:

x = 2. Pi/24 Range[0, 5];
data = Transpose[{x, Chop@Sin[x]}];

Grid[data, Alignment -> {"."}]

Grid with columns aligned on decimal point

Now I want to prepend a row to the grid with its two items centered. I tried the following, which if I understand the documentation, ought to do it:

Grid[Prepend[data, {"x", "sin x"}], Alignment -> {Center, {"."}}]

Grid with header row, original rows misaligned

But that just centers all entries in each column.

How do I get just the first row’s entries to be centered but the remaining rows to be aligned on the decimal point?