Definition: Hyperbolic Sine

The real hyperbolic sine function is a function defined using the real exponential function by the formula

\[\sinh(x):=\frac 12(\exp(x)-\exp(-x))\]

for all \(x\in\mathbb R\). Note that $\cosh$ can be interpreted as the "half the difference" of $\exp(x)$ and $\exp(-x)$.

The following graph visualizes the hyperbolic sine function:

  1. Proposition: Sum of Arguments of Hyperbolic Sine

Propositions: 1 2 3 4

Thank you to the contributors under CC BY-SA 4.0!




  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983