0

While I was doing a math on paper today, I wrote

$$\arctan x\ \frac{x^2}{2}$$

As the expression is ambiguous, I tried to make it less so by writing

$$\arctan(x)\frac{x^2}{2}\tag{1}$$

Is $(1)$ clear enough or should I write the following:

$$(\arctan(x))\frac{x^2}{2}\tag{2}$$

$(2)$ seems redundant in my opinion.

tryingtobeastoic
  • 3,176
  • 5
    I like Misha's approach if you are set on avoiding parentheses entirely. If you want to be clear but sparing of parentheses and keeping your expression in the same "order", then $(\arctan x)\frac{x^2}{2}$. – hardmath Feb 11 '22 at 06:15

2 Answers2

8

Why not write $\frac{x^2}{2} \arctan x$? Something like $\arctan(x)\frac{x^2}{2}$ seems clear to me, but still slightly unusual, and usually people put trig-style functions at the end of every term, just to avoid this sort of problem.

Misha Lavrov
  • 142,276
4

Expression $(1)$ is clear enough in my opinion, in the sense that you can read it as "everything I use as an input is between the parentheses."

Expression $(2)$, while cumbersome, is completely unambiguous. There is a degree of redundancy there, but making things unambiguous tends to make the notation more cumbersome -- it's a tradeoff.

However, I second Misha's suggestion of writing

$$\frac{x^2}{2} \arctan(x)$$

Usually whenever I have a function like that in a term -- be it $f(x)$, $\sin(x)$, $\exp(x)$, $\zeta(x)$, who knows -- it feels more natural to put everything that is not like that to the left of the function. That way there is no still ambiguity as to what is and isn't an argument of the function.

PrincessEev
  • 43,815