A
frothy function in
laymans' terms is a function that maps a
rational number "x" onto an
irrational number and vice versa, with either a finite number of exceptions across
the range of values of x or a finite number of exceptions over a
period of the function.
It's been proven that the cosine function satisfies the first
condition to be a frothy function, that is, it maps a
rational number θ given in degrees onto an irrational
number except for a few points.
The converse has not been
proven so it not known whether a cosine function is a true
frothy function. But if it were, that would be a very interesting thing, because the cosine is at the heart of
much mathematics.