I went down the etymologic rabbit hole and found out how sine actually got its name. And… it actually makes more sense than I expected. So, sorry if I called anyone an asshole before. Nevertheless, I stand by it: It would make more sense to call cosine sine and sine cosine, since cosine is more important and more natural than sine – as I elaboreted in-depth in this post.
But let’s start at the beginning of the etymologic rabbit hole…
Greeks, Arabs, Indians or Roman?
As you might know from history class, these are some of the great ancient civilizations and most of them happened to be great in math as well. Therefore a lot of mathematical concepts stem from them. The word ‘sine’ comes from the latin word ‘sinus’, which means ‘bay’ or ‘fold’, and more specifically ‘the hanging fold of a toga over the breast’. The translation from Latin to English was made in the 16th century – so actually copied from the Ancient Romans.
However, they didn’t not come up with the concept of sine either. In the 12th century AD the Romans translated the word from Arabic. The Arabs used the word ‘jayb‘ (جيب) or ‘jība. And here it gets messy… At first, they used the word ‘jība’, which itself is meaningless, but since Arabic is written without short vowels ‘jība’ was written as ‘jb’. This however was interpreted as the homograph ‘jayb‘ (جيب), which means ‘bosom’, ‘pocket’, or ‘fold’.
Neverthless, the Arabs weren’t the first either. It were the Indians likely around the 6th century AD, who used the word ‘jyā‘ or its synonym ‘jīvá‘, which means… (*drum-roll*) bow-string. I want to highlight the fact, that a bow-string is not the same as a bow, or a ‘fold’ or a ‘bay’. So, the meaningless translation in Arabic to the word ‘jība’, which later on was interpreted as ‘jayb‘ (‘bosom’, ‘pocket’, or ‘fold’) is really to blame for the confusion and misinterpretation of the word sine.
Nevertheless, a bow still got something to do with a bow-string, so we’re not that far off. However, a bow-string is the better word for sine and here’s why…
The Alternative to the Unit Circle
The Indians did not use the unit circle as it is common today, when they explored trigonometry. Instead they used an arch or as one could imagine in these times – a bow. Now, if look at the “bow-string” in the figure below (point A to B), you almost got your sine relation. If you cut this line in half (point A to C) and divide it by the radius (point O to A) you get sine of the angle θ.
I assume they discovered sine first, since it’s easy to get to it by looking at a bow / bowstring. Also, the name itself makes kinda sense. Even though, correctly it is a half bowstring. So, actually we should call sine ‘half sine’.
What it comes down to
It comes down to one of my most hated saysings in German:
Es ist historisch gewachsen.
Which means, it grew historically. To me this is just a poor excuse or just another way of saying: “It actually would make sense to do it differently today, if we started from scratch. However… (sigh) It just isn’t worth the effort.” And most of the time, if you actually think it through, you have to agree. Also in this case.
My recommendation knowing now what I know: Let us call cosine ‘fletch’ or ‘fin(e)’ – as in the end of arrow and continue to call sine ‘sine’, but put it second place.
My unreliable sources:
- English Stack Exchange: What reasoning is behind the names of the trigonometric functions “sine”, “secant” and “tangent”?
- HSM Stack Exchange: Where does the word sine (as in sin x) come from?
- Etymology of ‘Sine and Cosine’, Wikipedia
- HSM Stack Exchange: What is the etymology behind sine, cosine, tangent, etc.?
- Quora: From where do the names sine, cosine, tangent and cotangent come from?
