3 Transcendental functions
3.1 Concepts
The mathematical description of physical phenomena often involves functions other
than the algebraic functions discussed in Chapter 2. The most important of these
transcendental functions are the trigonometric functions, discussed in Sections 3.2 to
3.5, and the exponential function and its inverse function, the logarithmic function,
discussed in Sections 3.6 to 3.8. Other functions are defined in terms of these
‘elementary functions’, and a brief description of the hyperbolic functions is given in
Section 3.9.
Some applications are illustrated in Figure 3.1. Three of these involve
trigonometric functions. Trigonometry as a distinct branch of mathematics has its
origins as a tool for the construction of astronomical tables. It is concerned with the
use of trigonometric functions for the solution of geometric problems involving
Figure 3.1