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I'm currently learning about hyperbolic trig functions, and i don't really get the point. At first, I found it really weird that the input is the area divided by 2, and just wondered what was the point of it anyways?

So, are there any real world applications for this kind of stuff?

Agrim Rana
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  • https://en.wikipedia.org/wiki/Catenary. In addition, hyperbolic trig functions can be viewed as trig functions of imaginary angles, and vice-versa, which among other things gives a way to interpret Lorentz transformations. These functions show up in many other contexts as well. – amd Nov 27 '19 at 00:04
  • At least one: the shape of a chain hanging from two walls at its extremities under the action of gravity is a hyperbolic cosine, whence the name of catenary for this curve. – Bernard Nov 27 '19 at 00:05
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    Those who study hyperbolic (non-Euclidean) geometry use the functions regularly. – Blue Nov 27 '19 at 00:06
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    I would add special relativity as a field where hyperbolic geometry is important. – JG123 Nov 27 '19 at 00:06
  • As a pre-calc student -- not much application for these functions. You can use them to perameterize a hyperbolic curve, and they describe a centenary curve (like the gateway arch in St Louis.) They have their use in Calculus, though. – user317176 Nov 27 '19 at 00:07
  • Note that trig and hyperbolic functions are just special cases of the exponential. More precisely, $\cosh x$ is the even part of $e^x$, $\sinh x$ is the odd part. Likewise for $\cos x$, $\sin x$ and $e^{ix}$. While that does not tell you how useful they are, at least it shows there is nothing really new here. – Jean-Claude Arbaut Nov 27 '19 at 00:08
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    When you study some of the properties of these functions, you would come to see their elegance. Question is similar to:https://math.stackexchange.com/questions/123/real-world-uses-of-hyperbolic-trigonometric-functions – NoChance Nov 27 '19 at 00:08

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From the Wikipedia page on hyperbolic functons:

Hyperbolic functions occur in the solutions of many linear differential equations (for example, the equation defining a catenary), of some cubic equations, in calculations of angles and distances in hyperbolic geometry, and of Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity.

Randy Marsh
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