1

I am curious whether there exists one, like an extension to the PEMDAS rule. I am referring to trigonometric, logarithmic, and other functions similar. This is because I am confused about when to drop grouping symbols.

For instance, we understand that for an arbitrary $c$, in the expression $\sin cx$, $cx$ is the 'input' to the sine function. But what about $\sin cxyz$? Whenever I see something like this, it is usually $\sin(cxyz)$ but not $\sin cxyz$. I am confused because we can let $a = cxyz$, hence $\sin a = \sin cxyz$.

Blue
  • 75,673
soupless
  • 2,344
  • 2
    The fact that in "cxyz" the letters have no space between them tells you that they are to be treated as a single variable. But I agree that "sin cxyz" would be better written sin(cxyz). You can never have too many parentheses! – user247327 Jun 01 '21 at 12:43
  • 1
    I disagree that missing spaces mean that it's to be treated as a single variable. It simply means that you take their product. You should refrain from using multiletter variables. Or if you have to, at least write them upright instead of cursive (like $\sin$ instead of $sin$). – Vercassivelaunos Jun 01 '21 at 12:48
  • Is incorrect to skip using brackets even for trigonometric functions. Example:$\sin \pi +\pi=0 \lor \pi$. The reason brackets are skipped is for ease of notation where there is enough clarity regarding the argument of the function. – WindSoul Jun 01 '21 at 13:18
  • 1
    @WindSoul this is an aside, but "$\lor$" doesn't replace "or" in every way that "or" is used in English. It goes between things that have truth values, which "$\pi$" doesn't. – Mark S. Jun 01 '21 at 13:30
  • The plain translation of that expression is “sine of $\pi$ plus $\pi$ is either zero or $\pi$”. – WindSoul Jun 01 '21 at 13:52
  • 2
    It is primarily the responsibility of the person writing anything to write it clearly so that there is less room for confusion. If in doubt use parentheses. Even with the PEDMAS rule one shouldn't assume readers to be aware of it (or be efficient at applying it) and hence it makes sense to add parentheses when the expression looks complicated. – Paramanand Singh Jun 01 '21 at 15:37
  • @WindSoul When $\vee$ is placed between numbers, it often denotes the maximum, so $0\vee\pi=\pi$. – Sandejo Jun 04 '21 at 03:14

1 Answers1

1

The wikipedia page on trigonometic identities provides a good summary of the common practice. Thus it looks like one omits parentheses only when the argument occupies the width of one symbol. Thus $$ \sin x \quad \sin \frac{x}{2} \quad \sin(2x)\quad \sin(x + y) $$ Moreover, I agree with WindSoul that $\sin(x) -x$ is preferable to $\sin x - x$, although both are used on this site, as shown in this question and its answers.

J.-E. Pin
  • 40,163
  • Can I ask if this applies to other kinds of functions such as logarithmic, inverse trigonometric functions? – soupless Jun 04 '21 at 04:21
  • 1
    Yes. The general ides is to avoid ambiguity. Thus $\ln(xy)$ is preferable to $\ln xy$, although both are used. – J.-E. Pin Jun 04 '21 at 04:32