Despite the name, this function is not periodic, and it cannot be written in terms of sinusoidal or even hypergeometric functions.

Phase in sinusoidal functions or in waves has two different, but closely related, meanings.

The phase of an oscillation or wave refers to a sinusoidal function such as the following:

In a sinusoidal function such as , C represents the amplitude of the sound wave.

(Note: not to be confused with the reciprocal of the given sinusoidal function).

Solving the differential equation above, a solution which is a sinusoidal function is obtained.

All real world signals can be represented as an infinite sum of sinusoidal functions via a Fourier series.

The real-valued sinusoidal function representing either voltage or current may be broken into two complex-valued functions.

If the basis set of sinusoidal functions suit the behaviour being modelled, relatively few harmonic terms need to be added.

In this case the expansion consists of sinusoidal functions.