Date Column to DayOfWeek Column

Hi.

I've got a table that has a Date field in YYYY-MM-DD format and another column called DayOfWeek.  What I want to do is based upon the Date field the tsql will populate the DayOfWeek with the correct value.  The DATENAME(DW,'YYYY-MM-DD') does return the right value, but I can't figure out how to update the entire table...

Apologize for the noob question... Thanks.

- Michael