- #1
Jhenrique
- 685
- 4
Is known that in every rectangle triangle the following relationships are true:
But, how use geometrically the function sinh, cosh, and tanh?
But, how use geometrically the function sinh, cosh, and tanh?
SteamKing said: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 said:But I still don't understood how the hyperbolic functions help me to solve geometric problems.
micromass said:Why do you expect that they do?
Jhenrique said:Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.
Jhenrique said:Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.
Jhenrique said:But I still don't understood how the hyperbolic functions help me to solve geometric problems.
micromass said:Study hyperbolic geometry
Hyperbolic functions are mathematical functions that are used to describe the relationship between the sides and angles of a hyperbolic triangle. They are derived from the hyperbolic sine, cosine, and tangent functions, and are commonly used in non-Euclidean geometries, such as hyperbolic geometry.
In geometry, hyperbolic functions are used to calculate the lengths of the sides and angles in a hyperbolic triangle. They are also used to solve problems in hyperbolic geometry, such as finding the area of a hyperbolic polygon or the distance between two points on a hyperbolic surface.
Hyperbolic functions are similar to trigonometric functions, but they are defined for hyperbolic angles instead of circular angles. Hyperbolic functions are also related to the exponential function e^x, while trigonometric functions are related to the unit circle.
Yes, hyperbolic functions can be graphed. The graphs of hyperbolic functions have a similar shape to the graphs of trigonometric functions, but they are flatter and more spread out.
Hyperbolic functions have many real-world applications in geometry, such as in the design of curved structures, such as bridges and arches. They are also used in physics and engineering to model the behavior of waves and vibrations. Additionally, hyperbolic geometry is used in the field of computer graphics to create 3D models and animations.