I'm sure you used inverse of a cosine multiple times. Didactic math today is just not bothering to give it a name. Probably because people think that sin, cos and tan is enough. Even ctg which is just inverse of tan is often skipped.
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.
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.