Is known that in every rectangle triangle the following relationships are true: But, how use geometrically the function sinh, cosh, and tanh?
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)
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?
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.
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.