Exploiting the ambiguity of the notation $sin2x$ I have been wondering what would happen if someone had to solve an inequality like this 
$$2 \sin2x \le\sqrt{3}$$ 
And 'interpreted' it that way 
$$2\sin(2)x \le\sqrt{3}$$ $$\sin(2) > 0 $$$$x\le\frac{\sqrt{3}}{2sin(2)}$$
Do you think that the author of the test should have used parentheses and that the solution should be accepted or that $\sin 2x$ should always be treated as $\sin(2x)$?
 A: If we don't assume an adversarial context (!), then we should try to understand the intent, context, and sense of the question. Seems highly unlikely that $\sin 2$ often arises as a constant, while $\sin(2x)$ is very common. Thus, we conclude that it is the latter. If the writer intended the unusual $(\sin 2)\cdot x$, they'd presumably have emphasized this.
On the other hand, in the highly artificial and often adversarial and prankish situations of "school math", it is apparently best to be paranoid about bait-and-switch and similar, so you must ask. E.g., it might be that the (adversarial) examiner exactly wishes to prank you about precedence-of-operations (despite there being no genuine universal consensus). 
But, again, in real life math (as opposed to school math), the context should explain, or if not, you should (obviously!) take the "usual" interpretation ... and not think too much about formal "precedence" issues.
A: Functions in general are parenthesized and in cases where they are not I believe the student's hypothetical interpretation is sound, especially since there is a really nasty habit of doing this with trig functions in particular, e.g. $sin^2x$. Nevertheless, it is almost certain that such a question would be a problem based on very similar problems already under study prior to the test and the intended interpretation should be clear (which I am 100% certain is $\sin(2x)$); and, if it is not, then it is ambiguous, and the student should have asked for clarification.
