Answer:
x=60,150,240,330
Step-by-step explanation:
[tex]3 \cot(2x) = - \sqrt{3} [/tex]
[tex] \cot(2x) = \frac{ - \sqrt{3} }{3} [/tex]
Take the arc cot of both sides
[tex] \cot {}^{ - 1} ( \cot(2x) ) = \cot {}^{ - 1} ( \frac{ - \sqrt{3} }{3} ) [/tex]
[tex]2x = 120[/tex]
Remember cotangent has a period of 180 degrees
[tex]2x = 120 + 90(n)[/tex]
where n is 0, 1,2,3,4,5.....
Isolate x.
[tex]x = 60 + 90(n)[/tex]
where n is 0, 1,2,3,4,5,6.
Keep plugging in integers as long they are in the interval [0,360].
We get
60,150,240,330.
