function is a function that is not a root of a polynomial equation.
Such functions arise frequently in mathematics and science. A
function that is a root of a polynomial equation is an algebraic
function; all other functions are called transcendental.
The importance of transcendental functions stems from the
fact that most of the functions that describe natural phenomena
turn out to be transcendental functions. The six trigonometric
functions...-sine, cosine, tangent, cotangent, secant, and cosecant-are
all transcendental, for example, as are the logarithmic,
exponential, and hyperbolic functions.
William W. Adams 33