Real world uses of hyperbolic trigonometric functions I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful.
Is there any good examples of their uses outside academia?

Velocity addition in (special) relativity is not linear, but becomes linear when expressed in terms of hyperbolic tangent functions.
More precisely, if you add two motions in the same direction, such as a man walking at velocity $v_1$ on a train that moves at $v_2$ relative to the ground, the velocity $v$ of the man relative to ground is not $v_1 + v_2$; velocities don't add (otherwise by adding enough of them you could exceed the speed of light).  What does add is the inverse hyperbolic tangent of the velocities (in speed-of-light units, i.e., $v/c$).  
$$\tanh^{-1}(v/c)=\tanh^{-1}(v_1/c) + \tanh^{-1}(v_2/c)$$
This is one way of deriving special relativity: assume that a velocity addition formula holds, respecting a maximum speed of light and some other assumptions, and show that it has to be the above.
