[seanhunter]

I know what you mean, but as a sibling pointed out for everyone else's benefit, parent is using the word inverse where they mean reciprocal.

The inverse of cosine is arccosine (sometimes written acos or cos^{-1}). Secant is the reciprocal of cos ie sec x = 1/cos(x)).

Likewise cotan is the reciprocal of tan (1/tan). The inverse of tan is atan/arctan/tan^{-1}.

This is confusing for a lot of people because if you write x^{-1} that means 1/x. If you write f^{-1} and f is a function, then _generally_ it means the inverse of f. In the case of trig functions this is doubly confusing because people write sin^2 theta meaning (sin theta)^2 but sin^-1 theta means arcsin theta.

That's why in my maths studies they started by teaching you to do the inverse with a -1 so when you see it you don't get confused but changed to preferring arcsin etc as this is unambiguous and if you learn to write this way you won't confuse others.

[Rexxar]

It does not help that both reciprocal and inverse come from French, and that their common meanings are reversed in English. I'm not sure whether the meaning of both words has remained constant over time in these two languages, as they both roughly mean "the opposite" and if you want to avoid ambiguity, you simply add context. For example, if you say "inverse function" or "multiplicative inverse" it's not ambiguous.

Inverse function: https://en.wikipedia.org/wiki/Inverse_function / https://fr.wikipedia.org/wiki/Bijection_r%C3%A9ciproque

Reciprocal: https://en.wikipedia.org/wiki/Multiplicative_inverse / https://fr.wikipedia.org/wiki/Inverse

Wikipedia seems to have chosen "multiplicative inverse" over "reciprocal" for title, even though they are clearly indicated as synonymous.

[seanhunter]

That’s a really good point. I will try to remember to do that in future.