SOLUTION: Hi, I'm confused on how to approach this problem. It says to solve on the interval 0 <= theta < 2pi. Question: cotangent(2theta/3) = -square root 3 Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, I'm confused on how to approach this problem. It says to solve on the interval 0 <= theta < 2pi. Question: cotangent(2theta/3) = -square root 3 Thanks!      Log On


   

Question 1020360: Hi, I'm confused on how to approach this problem.
It says to solve on the interval 0 <= theta < 2pi.
Question:
cotangent(2theta/3) = -square root 3
Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Where is the cotangent negative?
1st quadrant:
+/+ = +
2nd qudrant:
-/+ = -
3rd quadrant:
-/- = +
4th qudrant:
+/- = -
---------------
So it can be in the
2nd or 4th qudrant
-----------------
+cot%28+2%2Atheta+%2F+3+%29+=+-+sqrt%283%29+
I can say:
+2%2Atheta%2F3+=+arccot%28+-sqrt%283%29+%29+
----------------------------
I know that +cot%28+pi%2F6+%29+=+sqrt%283%29+ so
+arccot%28++-sqrt%28+3+%29%29+=+pi+-+pi%2F6+
+arccot%28+-sqrt%283%29+%29+=+2%2Api+-+pi%2F6+
-------------------------------
+2%2Atheta%2F3+=+5%2Api%2F6+
+theta+=+%283%2F2%29%2A%28+5%2Api%2F6+%29+
+theta+=+15%2Api%2F12+
and
+2%2Atheta%2F3+=+11%2Api%2F6+
+theta+=+%283%2F2%29%2A%28+11%2Api%2F6+%29+
+theta+=+33%2Api%2F12+
--------------------------
Hope I got it!