The coyote in the picture is 'gaping', a form of intimidation or maintaining position in the pack structural order.
The coyote above doesn't seem to be too excited seeing as it's only giving a half-assed effort.
A coyote in full gape mode will, according to pictures I've seen and accounts I've read, be wearing that same facial expression but will have its' back hunched with its' hind feet just behind the fore feet and have its' tail tucked in tight against its' belly.
Usually only one coyote will gape while the other becomes almost immediately submissive. Because of that, the gape hardly ever results in an ass-whipping.
Okay. My sources are "The World of the Coyote" by Wayne Grady,
"God's Dog" by Hope Ryden,
and the hippie chick at the Great Valley Museum, Modesto Junior College.