ABSTRACT
This chapter describes a class of functions known as the hyperbolic functions which are very similar in some ways to the circular functions. It examines in detail what is meant by an inverse function. The chapter helps the reader to use the hyperbolic functions and their identities, and solve algebraic equations which involve hyperbolic functions. It assists the reader in differentiating hyperbolic functions, deciding when a function has an inverse function, and expressing inverse hyperbolic functions in logarithmic form. A practical problem is also analyzed concerning the sag of a chain. We shall also consider a practical problem concerning the sag of a chain. Bijections are comparatively rare, and so usually it is necessary to modify either the domain, the codomain or both in order to obtain a function which has an inverse.
