Evaluate sinh, cosh, tanh and their inverses for any real number input.
Hyperbolic functions are analogs of trigonometric functions defined using the exponential function: sinh(x) = (eˣ − e⁻ˣ)/2, cosh(x) = (eˣ + e⁻ˣ)/2, tanh(x) = sinh(x)/cosh(x). Their inverses are expressed in terms of logarithms.
Hyperbolic definitions
sinh x = (eˣ − e⁻ˣ)/2, cosh x = (eˣ + e⁻ˣ)/2
Inverse hyperbolic
arcsinh(x) = ln(x + √(x² + 1))
sin is circular (relates to the unit circle), while sinh is hyperbolic (relates to the unit hyperbola). sinh(x) = (eˣ − e⁻ˣ)/2 grows exponentially, unlike sin which oscillates between −1 and 1.
They appear in catenary curves (hanging cables), special relativity (rapidity), and solutions to differential equations like the heat equation.