what is really meant by hyberpolic function?

Question

i know that cosh x =(e^x+e^-x)/2 and etc.....
but what does that mean exacty?

Answer 1

OK, a hyperbola is a geometric figure that has two loci, and all the points that are part of the hyperbola have a consistent difference in distances to the two loci. IE, (distance to locus 1) - (distance to locus 2) is the same for all points.

Then some bright guy got the idea to create a "unit hyperbola" much like the "unit circle" that they use for circular trig functions (sin, cos, tan).

And then, on that unit hyperbola, you can create a right triangle using the x-axis and the point on the hyperbola, and calculate the same functions, opposite over hypoteneuse, etc. Except you're using a hyperbola, not a circle, so they're sinh, cosh and tanh.

Answer 2

various combinations of e^x and e^-x (called hyperbolic functions) occur so frequently in applied mathematics that that they have been given special names and have been thoroughly investigated by mathemeticians. Hyperbolic functions are so called because they are related to a rectangular hyperbola much the same way that trigonometric functions (also called circular functions) are related to the circle.

You could have asked "What is really meant by trigonometric functions"? and gotten a similar answer.

Answer 3

It simply means when graphed, it forms a hyperbola.

http://en.wikipedia.org/wiki/Hyperbolic_function

Answer 4

hyperbolic funcions are defined as such
sinhx=[e^x-e^x]/2 etc