Why is the 'argument' of a function named as such?

Question

When watching some videos on various bits of mathematics, I observed the word "argument" being used to describe what is in layman's terms 'the inside of the bracket'.

I can understand the use of the word 'argument' in the context of complex numbers; attributed to Jean Argand's work with complex numbers.

So for example, for the complex number $z= \cos \theta + i \sin \theta$, we say that $\theta$ is the argument of $z$. In this context, the use of the word "argument" makes sense because it is the input of the function as well as having some relation to the Argand diagram.

However, why is it used in a more general context of $f(x)$, where $x$ is then said to be the 'argument' of $f$?

Answer 1

Tracing the etymology of a word can be a difficult task. For what it is worth, the usage of the word argument as "the angle, arc, or other mathematical quantity, from which another required quantity may be deduced, or on which its calculation depends" dates back to 1405AD. Cite: the Oxford English Dictionary.

Answer 2

It is a term with two different meanings. In the case of functions, which have inputs and an output, the inputs are commonly called arguments or parameters. In the case of the complex plane (also called the Argand diagram) any complex number is uniquely determined if you know both its distance from the origin and the anticlockwise angle at which the vector from the origin makes with the real axis, and that angle is called the argument of the complex number, while that distance is called the modulus. (Yes "modulus" is another term with a different meaning in number theory.)