The Bayeux Tapestry wasn't stitched yet, because the story was only then being "finished" with William's coronation. But the BT could have been completed a year later. Most students/enthusiasts imagine that the last (who knows how many) feet of the BT depicted William's coronation, at the very least.

In Hypatia's posted pic, William looks angry and alarmed together: he is grabbing his sword because he hears the riot starting up outside. "The new King himself, for the first time in his life, was seen to be trembling: but with what emotion nobody knows". (David Howarth, 1066 the Year of the Conquest)