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Identification of a curious function

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ which is, as I understand, defined as $\sec(x) = \frac1{\cos x}$. During my studies, I never encountered this function.

I am wondering two things:

- How widespread is the notation $\sec x$? As I see it, it is completely standard notation in US schools, but not as common in Europe. Is there a historic reason behind this dichotomy?
- Is there a reason for calling the function $\sec$? Is there some geometric interpretation behind the name?

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First of all, the use of $\sec$ is standard in the United Kingdom which is part of Europe. The fact might be that $\sec$ is used in English-speaking countries, of which Slovenia is not.

The word Secant comes from a Latin word meaning “to cut”. This picture shows the definition of sine, tangent and secant. It justifies the naming of both the tangent and secant functions. This picture shows the co-functions, e.g. co-sine, co-tangent and co-secant.

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