Hyperbolic Functions

Evaluate hyperbolic sine, cosine, tangent, and their inverses.

Inputs

Input Value (x)

Function Values

1.1752

sinh(x)

Analogs of the ordinary trigonometric functions for a hyperbola.

cosh(x)1.5431

tanh(x)0.7616

Quick Reference

Inverse sinh0.8814

Inverse cosh0.0000

Inverse tanhUndefined

What are Hyperbolic Functions?

Hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using a hyperbola rather than a circle. They occur in many linear differential equations, such as the shape of a hanging cable (the catenary).

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Pro Tips

cosh²(x) - sinh²(x) = 1 (analogous to sin²θ + cos²θ = 1).
The graph of y = cosh(x) is called a catenary.
In special relativity, hyperbolic functions are used to represent lorentz transformations.

Fun Facts

"The Gateway Arch in St. Louis, Missouri, is designed in the shape of a weighted catenary (inverted hyperbolic cosine)."
"Hyperbolic functions were introduced in the 1760s by Vincenzo Riccati and Johann Heinrich Lambert."
"Engineers use hyperbolic functions to calculate stresses in suspension bridge cables."

Formula: sinh(x) = (eˣ - e⁻ˣ)/2, cosh(x) = (eˣ + e⁻ˣ)/2

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