Hyperbolic Functions

[lord loh.]

http://www.math.com/tables/trig/hyperbolics.htm

What is the physical interpretation of hyperbolic functions? sinh cosh tanh etc.

Just the way in a right angled triangle,

sin x= opp/hyp
cos x=adj/hyp
tan x=opp/adj

etc..

Thanks in advance.

 

[_3iMaJ]

They're related as follows: The reason you get nice relationships for cos(theta) = adj/hyp is due to pythagreon's theorem. a^2 + b^2 = c^2

take c = 1

a^2 + b^2 = 1, let a = sin x, b= cos x (from a definition below)

sin^2(x) + cos^2(x) = 1, so that leaves the sides of your triangle as the base cos(x) and the height sin(x) since your triangle can be inscribed in a circle. And in the image below, I've shown thats how they arise naturally. You can see how the rest falls out .

 

[_3iMaJ]

P.S. I had to do some digging for this. As I read this post I realized that no teacher in my history of highschool, college, or grad school has ever given a good definition of trigonomic functions to me. I had all the pieces but I needed to really think about how they all fit together. I understand now why they are periodic functions, and its all due to our friend Pythagoreous.