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.

The relationship between sine and cosine is apparent just by looking at the unit circle.