I’m a software engineer and I think one of my personal favorite random applications of Pythagoras/ trig was in my data visualization class back in scool. The assignment was to take a dataset of Soviet space launches with dogs and display it in an interactive approachable manner (ie less rigorous data science and more local science center), so I thought it would be fun to show rockets for each lauch and animate them rotating around the earth. Queue the trig to place each icon an appropriate distance (scaled to the launch height in my data), angle, and spacing from the earth.
I’ll admit it doesn’t come up all that often (in web development), but it’s nice to have that foundational knowledge to dredge up when I need it.
The etymology might help break down some of the nuance here
According to etymonline the etymology for expatriate (often shortened to expat) is:
Immigrate, is similar, but is more used to describe moving to a place:
The closer synonym to expatriate would probably be emigrate, the opposite of immigrate, to leave a place.
As to why one might use expatriate over emigrate; consider the sentence “I’m an American immigrant”. It’s kind of unclear if you’re trying to say that you are an American that has migrated to another country (as in “I’m an American immigrant living in Brussels”*), or someone who has migrated to America (as in “I’m an American immigrant from Slovakia”). Using expatriate removes the ambiguity: “I’m an American expatriate” and makes it clear that the speaker is trying to convey where they are from.
* technically, using emigrant here would be more clear, but English is a lawless and lazy language