# 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*.