Acetic acid or ethanoic acid - trivial names vs systematic names and correct formula representation My teacher likes to use household materials to do experiments. Today, we did an experiment that showed the reaction of vinegar and eggshell. 

When we were doing the analysis of the experiment, I realized that my teacher used the term acetic acid ($\ce{CH3COOH}$) instead of ethanoic acid. So, my questions are: 


What is the accepted usage for the terms acetic acid and ethanoic acid?
Which formula is the accepted representation of acetic acid, $\ce{CH3COOH}$ or $\ce{C2H4O2}$?
While I agree that the systematic name ethanoic acid makes a lot more sense, the name acetic acid has been used for so long that it's the accepted IUPAC name and is used almost universally. Both refer to the same compound.

Molecular formulas like $\ce{C2H4O2}$ are often seen when doing elemental analysis and the like, but give no structural information. $\ce{CH3COOH}$ makes it clear that it's an acid and shows the carbonyl group.