Geometry with hyperbolic functions

[Jhenrique]

Is known that in every rectangle triangle the following relationships are true:

But, how use geometrically the function sinh, cosh, and tanh?

 

[micromass]

Study hyperbolic geometry

 

[SteamKing]

This article gives one geometric interpretation of sinh and cosh:

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

(check out the figure at the upper RHS of the article)

 

[Jhenrique]

This article gives one geometric interpretation of sinh and cosh:

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

(check out the figure at the upper RHS of the article)

But I still don't understood how the hyperbolic functions help me to solve geometric problems.

 

[micromass]

But I still don't understood how the hyperbolic functions help me to solve geometric problems.

Why do you expect that they do?

 

[Jhenrique]

Why do you expect that they do?

Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.

 

[micromass]

Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.

OK. Which formulas don't you understand the deduction of? What is the deduction and what don't you understand about them?

 

[Jhenrique]

Look these formulas:

http://en.wikipedia.org/wiki/Elliptic_coordinates#Basic_definition

I don't understand because x and y are equals to these expressions.

 

[symbolipoint]

Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.

But I still don't understood how the hyperbolic functions help me to solve geometric problems.

Study hyperbolic geometry

This last one was said best.


Trigonometry is Geometry based on a unit circle.
Hyperbolic sines and cosines are based on the unit hyperbola.
Study the hyperbola and the exponential and logarithmic functions based on the Euler number base.

 

[Jhenrique]

I already studied and I continue don't understand how use it