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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.

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  • $\begingroup$ it is a useful notation abbreviation sometimes $\endgroup$
    – gt6989b
    Jan 31, 2019 at 21:44
  • $\begingroup$ 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. $\endgroup$
    – Jean Marie
    Feb 1, 2019 at 19:53

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If you're asking how they are defined then: $$\sec(x) = \frac{1}{\cos(x)}$$ and $$\csc(x) = \frac{1}{\sin(x)}$$

If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.

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    $\begingroup$ 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. $\endgroup$
    – Mark
    Jan 31, 2019 at 21:48

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