Practical application of hyperbolic functions?

Question

Mathematics

cosh();
sinh();
tanh();
In what cases do you use them and what common tasks are solved with their help?

Answer 1

Rarely applied. Mainly because they are well expressed through the usual exponent. Of course, writing (exp(x)+exp(-x))/2 is more difficult than cosh(x), but the function is usually needed not by itself, but as part of a larger expression.
Logic suggests that it is convenient to use hyperbolic functions for formulas that connect the angles and sides of a triangle on the Lobachevsky plane, but the same logic says that in real life this is needed a little less often than never. You can meet these functions in some heat conduction problems... and the answer is - use these functions when you meet them in the reference book. Of the other cases, I can only remember the use of tanh () in the formula for the relativistic addition of velocities. For some reason, it seemed convenient to me to switch from speed to "speed".
Well, a useful use of tanh() is that it maps the entire number line to the interval (-1,1). Although for positive numbers it's easier to use x/(1+x).

Answer 2

Hyperbolic tangent is used as an activation function in neural networks