I need to find cot(2x) = -1/sqrt(3) (where x = theta) for a rotation of axes problem I am doing.

This is how I tried to do it
cot(2x)=-1/sqrt(3)
tan(2x) = -sqrt(3)
tan^-1(-sqrt(3)) = -60 degrees
-60/2 = -30 degrees

The books answer is 60 degrees and I have no idea why

Question

I need to find cot(2x) = -1/sqrt(3) (where x = theta) for a rotation of axes problem I am doing. 

This is how I tried to do it 
cot(2x)=-1/sqrt(3)
tan(2x) = -sqrt(3)
tan^-1(-sqrt(3)) = -60 degrees
-60/2 = -30 degrees

The books answer is 60 degrees and I have no idea why

anonymous · Answer

I did one of the problems before this where I had to find theta for cot(2x) = 1/sqrt(3) and got 30 degrees which is correct

irishboy123 · Answer

you have a solution 2x = 120 also
this might be familiar
|dw:1445894142414:dw|
and these might help
|dw:1445894191867:dw|

i hope that helps:p