Hello there. I was having some trouble with a little question.
If cos(x)= 1/2 then x = arcos(1/2) which is pie/3.
Now if cos(x)= -1/2, is x=arcos(-1/2) still pie/3 or is arcos(-1/2) = 2pie/3?
Or are maybe both of them right? Thanks in advance.

You are correct that if \cos(x) = 1/2 then x = \frac 1 3 \pi. , although it could also equal \frac 5 3 \pi, because \cos (\pi/3) = \cos (5 \pi/3) = 1/2.. The complete set of solutions is:


\arccos (1/2 ) = \left { \pi/3 \pm 2 \pi n\\
\5 \pi/3 \pm 2 \pi n \right for n equals any integer.

If cos(x) = -1/2 then \arccos(1/2) = x = 2/3 \pi + 2 \pi n or x = 4/3 \pi + 2 \pi n. It can't be \pi/3 because we already know that \cos (\pi/3) = 1/2, not -1/2.