Byzantine is a good guess: Hipparchus was from a city about 50 miles away (Nicaea), though I think he did most of his work in Rhodes, and lived a few hundred years before the time of the Eastern Roman Empire. ;)

But anyway, the etymology helps: “sine” = medieval Latin translation of an Arabic corruption of a word originally from India and meaning “half a bowstring”. “Tangent” = touching. “Secant” = cutting. “Chord” = bowstring. See https://en.wikipedia.org/wiki/Jyā,_koti-jyā_and_utkrama-jyā

The reason sine and cosine are each-others derivative is that if you start with uniform circular motion and take the vector derivative, you get another uniform circular motion in velocity space.