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Recently I read an equation that was formated like the following one:

$f = \sin x y + \cos z$

Since $x$, $y$, and $z$ are different variables, and there are not brackets (), is $y$ inside the sin-operator or not? Does there exist some kind of rule for this?

Does it mean $f = \sin(x) y + \cos(z)$ or $f = \sin(x y) + \cos(z)$?

Lemonbonbon
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    Obviousdly, it means the second formula. Personally, I would write the first as $(\sin x)y+\cos z$. – Bernard Jun 30 '20 at 11:36
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    @Bernard or even better $y\sin x + \cos z$ – General Grievous Jun 30 '20 at 11:37
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    This is possiby somewhat context-dependent, but for me with trig functions the product has a higher precedence. A lot of physics and signal processing would become kludgy if we needed more parens in $\sin\omega t$ and $\sin2\pi f(t+t_0)$. In some contexts a case could be made for $\sin\omega t+\phi_0$ to mean $\sin(\omega t+\phi_0)$, but that would be a stretch. I think that the general rule, if any, is that parens can be dropped if the context makes the meaning clear. – Jyrki Lahtonen Jun 30 '20 at 11:40
  • @PankajTiwari: That's right. But maybe the O.P. prefers alphabetical order :-) – Bernard Jun 30 '20 at 11:41
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    Having said that, I have been somewhat guilty of assuming a reasonable level of context literacy from my students. I remember a particular calculus exam, where I described a Lissajoux curve $(\sin 2t,\sin 3t)$ and asked the students to plot it and the do basic differentiation. I was not happy to see one student plot $((\sin 2) t, (\sin 3)t)$. Either unwittingly or because that's what his calculator spewed out. It wasn't the first example of a Lissajoux curve, and my superiors absolved me, but... – Jyrki Lahtonen Jun 30 '20 at 11:44
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    More in the spirit of the excellent comments by Bernard and Pankaj Tiwari, I might handwrite $1/2x$ meaning $1/(2x)$. Simply because if I mean $(1/2)x$ I would ALWAYS write it $x/2$. Admittedly that is dangerously close to Humpty Dumpty territory :-/ – Jyrki Lahtonen Jun 30 '20 at 11:54
  • Thanks, excellent comments. I did not expect that. – Lemonbonbon Jun 30 '20 at 11:56
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    Please, be nice to me and always put the brackets even $\sin(x)$ – Claude Leibovici Jun 30 '20 at 13:29
  • What do you all think about $\mathbf{r}(t) = \cos\omega t , \mathbf{e}_1 + \sin\omega t , \mathbf{e}_2$? Clear or confusing? – md2perpe Jun 30 '20 at 13:35
  • @ md2perpe: This seems okay to me, since bold letters often indicate vectors, not scalar values. – Lemonbonbon Jun 30 '20 at 13:57
  • @md2perpe Looks clear to me. I cannot think of anyone misunderstanding that. – Jyrki Lahtonen Jul 13 '20 at 09:27

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Refering to the excellent comments under the inital question, I will answer my own question, just to mark this as answered. Therefore $f=\sin(xy)+\cos(z)$ is correct.

md2perpe
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Lemonbonbon
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