Work out hyperbolic sine instantly with clear inputs, formula shown and shareable results.
The hyperbolic sine is sinh x = (eˣ − e⁻ˣ)/2, the odd part of the exponential. It parametrises the unit hyperbola in the same way sine parametrises the circle, and satisfies cosh²x − sinh²x = 1.
Hyperbolic sine
sinh x = (eˣ − e⁻ˣ) / 2
Identity
cosh²x − sinh²x = 1
(e − 1/e)/2 ≈ 1.1752012.
In the catenary: a hanging chain follows y = a·cosh(x/a), and its arc length involves sinh.