# Geometry with hyperbolic functions

by Jhenrique
Tags: functions, geometry, hyperbolic
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 P: 686 Is known that in every rectangle triangle the following relationships are true: But, how use geometrically the function sinh, cosh, and tanh?
 Mentor P: 18,040 Study hyperbolic geometry
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,321 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)
P: 686
Geometry with hyperbolic functions

 Quote by 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)
But I still don't understood how the hyperbolic functions help me to solve geometric problems.
Mentor
P: 18,040
 Quote by Jhenrique But I still don't understood how the hyperbolic functions help me to solve geometric problems.
Why do you expect that they do?
P: 686
 Quote by micromass 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.
Mentor
P: 18,040
 Quote by Jhenrique 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?
 P: 686 Look these formulas: http://en.wikipedia.org/wiki/Ellipti...sic_definition I don't understand because x and y are equals to these expressions.
HW Helper
PF Gold
P: 2,796
 Quote by Jhenrique Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.
 Quote by Jhenrique But I still don't understood how the hyperbolic functions help me to solve geometric problems.
 Quote by micromass 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.
 P: 686 I already studied and I continue don't understand how use it

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