He has either coarsened the public discourse or reflected it, or perhaps both, depending on your view of him, but he is not alone. Society in recent years has embraced what used to be considered profanity. Even The New York Times, the so-called Gray Lady with all the news that’s fit to print, found it fit to print the B.S. word just 14 times in the many years before Mr. Trump’s inauguration, according to a Nexis search, but has used it 26 times since — not all in stories covering the president.

Other presidents, of course, have engaged in common language and found a connection to everyday people. Harry S. Truman was told to “give ’em hell, Harry,” to which he famously replied: “I don’t give them hell. I just tell the truth about them and they think it’s hell.” But in general, it used to be something of a mini-scandal when a president was caught cursing in public.

During a campaign event in 2000, George W. Bush was heard over a live microphone talking with his running mate, Dick Cheney, calling a Times reporter he did not particularly like a “major-league asshole.” In 2004, as vice president, Mr. Cheney told a senator on the Senate floor to “go fuck yourself.” His successor, Joseph R. Biden Jr., was overheard in 2010 using a variation of that profanity to tell Barack Obama what a big deal passage of health care legislation was.

Never has any president pushed the boundaries of language as far as Mr. Trump. He had a foul mouth long before politics, of course, but he seemed to try, however fitfully, to clean it up for a while when he set his sights on the White House. Still, he could not resist at times. At one rally during his 2016 campaign, he quoted a supporter calling a Republican rival, Senator Ted Cruz of Texas, a “pussy.”

Once taking office, he tried, at least, to keep it private, but he was uninhibited when the cameras were not on. After the special counsel, Robert S. Mueller III, was appointed, he told aides, “I’m fucked.” Speaking with lawmakers, he called African nations “shithole countries.”

Yet Mr. Trump feigned shock in January when the newly elected Representative Rashida Tlaib of Michigan said she and her fellow House Democrats were “going to impeach the motherfucker.” The president told reporters that “she dishonored herself” by “using language like that in front of her son and whoever else was there.”

Mick Mulvaney, the White House chief of staff, acknowledged a certain raw quality in Mr. Trump’s discourse but dismissed its significance. “The president does use coarse language in private a lot with us,” he told Jake Tapper on CNN after Ms. Tlaib’s comment. “Many people do.” But, he added, “I think there’s more important things as to who’s coarsening the language.”