Hello winsome

Do you understand what is meant by the word *domain* of a function? It is the set of *valid inputs* to that function. For example, the domain of \(\displaystyle \sqrt x\) is the set of non-negative numbers.

Now, as *papex* has said, \(\displaystyle \sin x\), and therefore \(\displaystyle \sin3x\) and \(\displaystyle -4\sin 3x\), are defined for all values of \(\displaystyle x\). In other words, the domain of these functions is the set of *all *real numbers.

There are various ways of writing this set. One is to use the symbol \(\displaystyle \mathbb{R}\). Another is to use interval notation: \(\displaystyle (-\infty, +\infty)\).

Grandad