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# Applications of Hyperbolic Trig Functions watch

1. I've not really been educated on the applications of hyperbolic trig functions (i.e. cosh(x), sinh(x)). Could anyone help me out?
2. Here are a few applications:

The curve is a catenary. Google it to find out about hanging chains and bridge archs.

The hyperbolic functions are connected to the trigonometric functions via complex numbers.

Alternatively, Google the Gudermannian function to find a direct connection between trigonometric and hyperbolic numbers. There is an interesting application here in the Mercator projection of the world map.

Vincenzo Riccati introduced the hyperbolic functions to solve cubic equations so there is another application there.

The rapidity of an object in special relativity is given by the formula .

The inverse sinh function is used to calculate the Roche Limit, the minimum distance at which a natural satellite may orbit a planet without being torn apart by tidal forces.

Many expressions involving the sum or difference of two squares can be integrated by making a hyperbolic substitution.

The parametric equations of the right hand branch of the unit rectangular hyperbola are and .

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Updated: February 9, 2010
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