Your use of "facetious" in that context is misguided. To say that facetious means frivolous is to miss the subtleties of both words. If you meant "frivolous" (which would make more sense in your thread title) then you should have used that word.
Most of my life and education were pre-Google. One reference of choice,
A Dictionary of Modern English Usage (1978 edition) by H.W. Fowler, has a very interesting discussion of words that mean jocose or jocular, i.e. arch, facetious, flippant, jesting, jocose, jocular, merry, waggish.
Fowler says (among other convoluted but fascinating things) that
"...these words are difficult to separate from each other; the dictionaries establish no very clear or serviceable distinction... attention is drawn merely to the points of difference." He goes on to explain several words, including:
"facetious (opp. solemn) implies a desire to be amusing; formerly a laudatory word, but now suggesting ill-timed levity or intrusiveness or the wish to shine."
I regret now that I took such a frivolous approach to my Latin class in 9th Grade. I needed Professor Google to help me with the following :
Habetis bona deum!
Vah! Denuone Latine loquebar? Me ineptum. Interdum modo elabitur.