Helpful Tools for Calculus, Chapter 1: Functions and Relations
Previous Section: 1.11 Elementary and Composite Functions
Forms
Hyperbolic functions are made of special combinations of the function ex. They are often compared to the trigonometric functions because of their similar identities, patterns, and formulas. Even their names are based on trigonometric functions, for example the two base hyperbolic functions are called hyperbolic sine and hyperbolic cosine. They are often referred to as “sinch” and “cosh” because of the long names and can be written as:
Just as there are four other trigonometric functions, there are also four other hyperbolic functions:
tanhx=sinhx/coshx cothx=coshx/sinhx sechx= 1/coshx cschx=1/sinhx
Example 1: Evaluate sinh(2)
Solution:
Example 2: Evaluate coth(0)
Solution:
So coth(0) is undefined.
There do exist hyperbolic inverse functions. They would be denoted with the standard f-1 notation, or with arc like arcsin(x), and most of which are well defined. The inverses won’t be discussed further here.