# Why are $\text{versin}(x)=1-\cos(x)$, $\text{coversin}(x)=1-\sin(x)$, $\text{vercosin}(x)=1+\cos(x)$ no longer used in maths?

I was preparing for a calculus exam and I came across the Wikipedia article for all the trigonometric identities. There I came across some terms that I had never seen before. They were: $$\text{versin}(x)=1-\cos(x)$$, $$\text{coversin}(x)=1-\sin(x)$$, $$\text{vercosin}(x)=1+\cos(x)$$ and other similar ones.

In the article it states that these were historically used but nowadays they have no real use. Why is that? Why are these not used anymore?

• Could that be a question for hsm.stackexchange.com? Commented Jan 24, 2021 at 15:45
• I woul assume it is much simpler to write $1-\cos(x)$ than $\operatorname{versin}(x)$.
– user
Commented Jan 24, 2021 at 15:45
• It's not that they're not "used", but that nobody cares to give them special names. For example, $\cos^2(x) = (1+\cos(2x))/2$ and $\sin^2(x) = (1-\cos(2x))/2$, so you could write the numerators in these formulas in terms of vercosin and versin, but it's irrelevant. Just write $1 \pm \cos(2x)$ and that's fine. It certainly is clearer. Anyway, the more important page about wacky trigonometric functions is theonion.com/….
– KCd
Commented Jan 24, 2021 at 15:46
• Perhaps special tables were initially created for these functions because 100+ years ago there were no calculators, and therefore a need was felt to have a look-up tables of values of $1 \pm \cos(\theta)$ and similar stuff. But with calculators widely available to students for 40+ years, such data is unnecessary to collect in a separate way.
– KCd
Commented Jan 24, 2021 at 15:48
• @KCd Hmmm. That is quite possible. In the article it mentions that these identities were used for sailing and related measurements. I think your second comment touches up on the really nicely. Commented Jan 24, 2021 at 15:52