Not sure if I wrote out the answer correctly, please help.

[isammc]

____

2 cos theta + sqrt3=0
2 cos theta =-sqrt3
cos theta =-sqrt3/2

210degrees = 7pi/6
150degrees = 5pi/6

My question is this: Should the answer be merely ( 7pi/6 or 5pi/6 ) OR should the answer be ( 7pi/6 + k pi, k E Z or 5pi/6 + 2k pi, k E Z ) ?
Also, if the second choice is correct; why?

 

[pka]

View attachment 1328
My question is this: Should the answer be merely ( 7pi/6 or 5pi/6 ) OR should the answer be ( 7pi/6 + k pi, k E Z or 5pi/6 + 2k pi, k E Z ) ?
Also, if the second choice is correct; why?

The second choice is correct because you were told to give the answers in that form.

The reason is \(\displaystyle \cos(\theta)=\cos(\theta+2k\pi),~\ {\forall k \in \mathbb{Z}.\)