Since math is a minimalistic science, what's the idea of defining such a thing like cosecant or secant? [duplicate]

As we all know, math is a minimalistic science. For example we don't put into the definition of differentiable functions that they have to be continuous. So my question is this:

What's the idea of defining such a thing like cosecant or secant? I have never seen their use in math or other science.

• it is a useful notation abbreviation sometimes Jan 31, 2019 at 21:44
• It would be interesting to see in which "mathematical geographical areas" sec and cosec are still used. For example, in France, they aren't used, and as far as I know they have never been used. Feb 1, 2019 at 19:53

If you're asking how they are defined then: $$\sec(x) = \frac{1}{\cos(x)}$$ and $$\csc(x) = \frac{1}{\sin(x)}$$
• I think OP means that these specific names $sec$ and $csc$ are not really used, we usually write $\frac{1}{cosx}$ and $\frac{1}{sinx}$ instead. And he is right. I never used $sec$ and $csc$, these names only confuse me. Defining sine, cosine and tangent is enough for everything.