"trace its origins" is correct and usable in written English.
You can use this phrase to refer to the process of finding out where something came from or how it started. For example, "We must trace its origins to determine where this issue began."
Poundworld, which has its headquarters in West Yorkshire, was formed in 2004, but it says it can trace its origins "back to 1974 and a market stall in Wakefield, West Yorkshire".
The company was officially founded in 1924, but it can trace its origins back to 1812, the date of a document in Giacomo Loro Piana's name.
The NPC of the presaccade eye position close to the saccade did not allow us to trace its origins because it occurred long after the presaccade eye position was acquired.
It's hard to trace its origins, and hard to control where it flows: Consider the case of Hervé Falciani, a former employee of HSBC Private Bank.
If the Circus Maximus sneaker can trace its origins to anyone, it is Christian Louboutin, who was similarly taken by surprise a few years earlier.
It does, however, trace its origins to a pope.
The band can trace its origins to 1887, when it was formed from the volunteer band of the 2nd Battalion, Prince Albert's Somersetshire Light Infantry.
But Apple has a strong technological case for updating the headphone jack, which can trace its origins back to at least 1878 and was originally used in old-fashioned telephone switchboards.
According to Juan Mendez (a UN Special Advisor who was himself tortured during the Argentinean military dictatorship): "Torture became systematic and pervasive during the military dictatorships of the 1970s and 1980s, but it would be a mistake to trace its origins only as far as this dark era.
Electronic mail can trace its origins to academic and military initiatives in the 1960s, though it didn't enter the mainstream until the mid-'90s, with AOL Mail (1992), Microsoft HoTMaiL (its original styling, in 1996) and Yahoo Mail (1997).
I'll describe the Uncanny in plain language, trace its origins back to Descartes and medieval automata, and show how it relates to our contemporary human fear and fascination with a broad variety of technologies from AI to cosmetics to robots to Siri to Google Glass to zombies.
