I have this expression $$\sin ( (x-y)\pi )\; \cos ( (x+y)(a-\pi )) \qquad (1)$$
Is it clear if I omit those external parentheses and write it like this? $$\sin (x-y)\pi \;\cos (x+y)(a-\pi ). \qquad (2) $$
In general, which one is preferred?
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1I would prefer $(1)$ in both cases – SolubleFish Jul 13 '21 at 10:30
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It looks like $\sin{x-y}$ is being multiplied by $\pi$ which is not what is intended from the first form. – John Douma Jul 13 '21 at 10:30
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You might try $$\sin\bigl((x-y)\pi\bigr)\cdot \cos\bigl((x+y)(a-\pi)\bigr). \qquad (3)$$ – Michael Hoppe Jul 13 '21 at 10:37
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See also https://math.stackexchange.com/questions/544360/should-i-use-parentheses-when-writing-log/544563#544563 – Michael Hoppe Jul 13 '21 at 11:10
4 Answers
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If the $\sin$ or $\cos$ function has only $1$ variable as an input then in many cases people just don't use the parentheses.
You might have seen $\sin x$ or $\cos x$ etc.
But in the example you have given, people will actually prefer the parentheses.
Because not only there are $2$ variables but a product going on.
If you write $\sin(x-y)\pi\cos(x+y)(a-\pi)$
Then people might confuse, are you trying to say $\sin((x-y)\pi)$ or $\pi\sin(x-y)$ which are obviously not equal in general.
Where writing $\sin((x-y)\pi)$ clearly says what it means.
Star Alpha
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Remember that a nice way to avoid confusion is writing $\sin(xy)$ instead of $\sin(x)(y)$ which may easily with confused with the product of the functions $\sin x$ and $y$.
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As said above, the second form is not clear at all, also as F. Ahmad Mala said, writing $\sin{x}y$ is not a good idea, adding to what he said, if you don't want pharanteses for some reason it is better to write it as $y.\sin{x}$.
Ata
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I prefer the first version. In fact, I would insist on it. As a general rule, I enter expressions in a form that would be correctly interpreted by mathematics software or as a line of computer code. Your second version would fail that test. I may appear to be taking directions from our machines, but it is important to avoid ambiguous expressions.
I notice that I now have parentheses around the argument of a trigonometric expression (e.g., sin(50°), not sin 50°) even in my had-written work. I do not believe I wrote that way 50 years ago, but I cannot even remember.
Pope
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