transcendental function

A transcendental function is a function that cannot be expressed algebraically, i.e. as algebraic function. For example, sin x (see sine) cannot be expressed in algebraic terms and hence, if f(x) = sin x, f(x) is a transcendental function. Transcendental functions are represented by transcendental curves.


The following transcendental functions are used in elementary mathematics.


Exponential functions. For example, y = a x, y = e x, y = e x.


Logarithmic functions (inverse functions of the exponential functions). For example, y = log x, y = ln x, y = log (x 2 – 1).


Trigonometric functions, also known as circular functions. These are: y = sin x, y = cos x, y = tan x, y = sec x, y = cosec x, and y = cot x.


Inverse trigonometric functions: y = sin–1 x, y = cos-1 x, y = tan–1 x, y = sec–1 x, y = cosec–1 x, and y = cot–1 x.


Hyperbolic functions: y = sinh x, y = cosh x, y = tanh x, y = sech x, y = cosech x, and y = coth x.


Inverse hyperbolic functions: y = sinh–1 x, y = cosh–1 x, y = tanh–1 x, y = sech–1 x, y = cosech–1 x, and y = coth–1 x.