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 = ax, y = ex, y = ex.
Logarithmic functions (inverse functions of the exponential functions). For example, y = log x, y = ln x, y = log (x2 - 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.