Retroactive Precognition

I already went further ahead in time to see what else happens. I've backtracked everything to this one event, that's why we're here today to prevent this incident from ever happening!

—Doctor Emmett Brown, Back to The Future II

Who needs precognitive powers when you've got Time Travel?

A character goes back to the past. From the other character's point of view, they seem to say, do and know things that imply a frighteningly accurate knowledge of the future. Of course, they do not need special powers to be able to do this—they only need to remember, because they have already lived though it before.

A variation is a character who is Trapped in the Past before their actual date of birth, but in a period that they are familiar with from history books. They may also be able to make use of a Convenient Eclipse if they remember the exact date when it is due to happen.

Note that you should not even attempt this without significant historical research under your belt, and even then, people have messed around with historical dates so often during the times and truth intermingled with myth so much that it will probably not do you a lot of good anyway. (We would also mention things like the language barrier, but those belong to the main Time Travel trope.)

Not to be confused with "retroactive clairvoyance", an entirely different term that has been used for the act of retrofitting vague predictions to events that have already happened.

If the character relies on science and engineering from the future, rather than knowledge of the current time period, they are Giving Radio to the Romans.

Examples of Retroactive Precognition include:

Comic Books

• Layla Miller of X Factor knows stuff because a version of herself traveled eighty years into the future and learned stuff and then told her past self.
• In modern age comics Barry Allen and many of his family member know the future, at least in vague terms, due to spending so much time in the 31st century. Barry himself was able to make use of this knowledge even after his death by time traveling to important events while he was still alive.

Film - Live-Action

• Done frequently in Back to The Future, as Marty accidentally blurts out the fates of the people he's meeting in the past.

"That's right, he's gonna be mayor!"

Literature

• In Lest Darkness Fall, 1930s archaeologist Martin Padway is mysteriously transported to 6th Century Italy (where the "Dark Ages" are about to come down with a vengeance). He is able to use his knowledge of classical history to pull this off a good deal.
• In Time Enough for Love, this is how archprotagonist Lazarus Long hopes to survive and prosper in the 1920's United States, since that's when he grew up and he has extensive period and personal knowledge of the era. Two things foil him: first, he arrives too early due to a miscalculation and winds up in 1917, on the cusp of U.S. involvement in World War I. Second, he falls in love with his mother Maureen and, in a misguided attempt to impress her, enlists in the army. However, he does entrust to Maureen a wealth of information on the future history of the United States in that timeline, allowing her to quietly abet several key events that help things turn out the way they should.
• Time Scout's scouts and guides really want to take advantage of this. They want to see and observe important historical events first hand. In the series, the only time it's deliberately taken advantage of is by the Ripper Watch Team, finally learning who Jack the Ripper was.
• In Warrior Cats, a bunch of characters are shocked when the time-traveling main character tells them where humans will build a barn and that off in the mountains there's a place they can live. Turns out that he's just speaking from his own experiences; he's far in the past.

Live Action TV

• On Babylon 5 all the various Minbari prophecies were actually made by Sinclair, who traveled into the past and became Valen. The prophecies simply predict what he knew would transpire in the future.
• Doctor Who, both old and new, does this all the time. In particular, the Third Doctor frequently remarked on how "primitive" Earth technology was during his exile in the 1970s.
• Quantum Leap invokes this trope on occasion. For example, once Sam made a bet that Gerald Ford would trip going down the stairs out of Air Force One, which, of course, then happens.
• Lost Season 5 did this a lot once the Time-Travel started.

Video Games

• In Chrono Trigger, Magus ends up in the past (ironically, coexisting with himself when he was a young boy), and uses his knowledge of the future (which he experienced as a young boy) to gain himself the position of a prophet in the royal palace.
• Archer in Fate/stay night knows all about Shirou's abilities, how he will injure himself with projection, the identities of Heroic Spirits who haven't revealed themselves, Saber's backstory, what the Grail really is, etc. Hint: He's Shirou from the future, so he not only lived through what is basically the Fate path, he's also had time to research on people he saw then like Caster and then correctly identify her as Medea. He also knows lots about the Big Bads' plots before they implement them and whatnot.
• A key gameplay mechanic in Radiant Historia, where the protagonist has the ability to jump to certain times and places in his life in order to Set Right What Once Went Wrong. Gets a double-dose because there are two timelines which are linked together, so progress in one provides hints as to events that may occur in the other.

Web Comics

• The time-traveling Cassie Wells of Times Like This has used warnings from her future self to stay away from bad mistakes ... such as knowing ahead of time which men in a bar are safe to cruise, and which are married, potential date-rapists, or otherwise trouble. She deliberately avoids telling herself who she will fall in love with for good, afraid that if she knows, she'll screw it up. And the fact that no one has shown up from the future to tell her, suggests that her willpower is fairly strong on this point.