Introduction
The hyperbolic functions , etc are certain combinations of the exponential functions and . The notation implies a close relationship between these functions and the trigonometric functions , etc. The close relationship is algebraic rather than geometrical. For example, the functions and satisfy the relation
which is very similar to the trigonometric identity . (In fact every trigonometric identity has an equivalent hyperbolic function identity.)
The hyperbolic functions are not introduced because they are a mathematical nicety. They arise naturally and sufficiently often to warrant sustained study. For example, the shape of a chain hanging under gravity is well described by and the deformation of uniform beams can be expressed in terms of tanh .
Prerequisites
- have a good knowledge of the exponential function
- have knowledge of odd and even functions
- have familiarity with the definitions of and of trigonometric identities
Learning Outcomes
- explain how hyperbolic functions are defined in terms of exponential functions
- obtain and use hyperbolic function identities
- manipulate expressions involving hyperbolic functions