# Geometry with hyperbolic functions

1. May 17, 2014

### Jhenrique

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

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

2. May 17, 2014

### micromass

Staff Emeritus
Study hyperbolic geometry

3. May 17, 2014

### SteamKing

Staff Emeritus

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

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

4. May 17, 2014

### Jhenrique

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

5. May 17, 2014

### micromass

Staff Emeritus
Why do you expect that they do?

6. May 17, 2014

### Jhenrique

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

7. May 17, 2014

### micromass

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

8. May 17, 2014

### Jhenrique

9. May 17, 2014

### symbolipoint

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.

10. May 18, 2014

### Jhenrique

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