3 ms·
I found sine and associated concepts to be arcane and Byzantine when learning then through algebra and geometry alone. Seeing sine, cosine, etc as merely each
by stephengillie 9y ago
I found sine and associated concepts to be arcane and Byzantine when learning then through algebra and geometry alone.
Seeing sine, cosine, etc as merely each other's derivative was astonishing and eye opening. So elegant. It made me love math again.
- jacobolus 9y agoByzantine 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 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.
- trentmb 9y agoThe relationship between sine and cosine is apparent just by looking at the unit circle.