In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse …

Nov 4, 2024 · Learn the inverse hyperbolic trigonometric functions with graphs, proofs, and examples.

Dec 3, 2025 · The inverse hyperbolic functions, sometimes also called the area hyperbolic functions (Spanier and Oldham 1987, p. 263) are the multivalued function that are the inverse functions of the …

Jul 23, 2025 · There are six inverse hyperbolic functions, namely, inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic …

We were introduced to hyperbolic functions previously, along with some of their basic properties. In this section, we look at differentiation and integration formulas for the hyperbolic functions and their …

We can derive differentiation formulas for the other inverse hyperbolic functions in a similar fashion. These differentiation formulas are summarized in the following table.

Figure 7.4.3 shows the restrictions on the domains to make each function one-to-one and the resulting domains and ranges of their inverse functions. Their graphs are shown in Figure 7.4.4.

Explore inverse hyperbolic functions in trigonometry with definitions, derivations, identities and applications in calculus and physics.

Each of the six functions is a multivalued function of z. Arcsinh ⁡ z and Arccsch ⁡ z have branch points at z = ± i; the other four functions have branch points at z = ± 1. See Levinson and Redheffer (1970, …

All of the hyperbolic functions have inverses for an appropriate domain (for cosh and sech , we restrict the domain to x 0. The rest hold for all real numbers.). The four we will use most often are: 2 . e x …