parenthesis ,or without parenthesis? I have the following function: $$f(x)=\sin2x;-\pi\leq x<-\frac{\pi}{2}$$ if i consider 2 within parenthesis $\sin[2(-\pi)]$, it is equal to $0$. if i do not consider 2 within parenthesis $\sin2(-\pi)$, it is equal to $-2.856642116$. Why does the result vary? Which one will I consider for my given exercise? Parenthesis ,or without parenthesis?

For your exercise, it is certainly $\sin (2x)$. Like what the commenter mentioned above, your calculator/computer interprets the one without parentheses as $(\sin (2)) \cdot (\pi)$. But if this is what is wanted from you, it should've been written $x \sin 2$ instead, to avoid ambiguity.