Solve sqrt(cot x) = 3^(1/4) in [0, 2π)

[Aaron H.]

Homework Statement

Solve, finding all solutions in [0, 2pi)

Homework Equations

sqrt (cot x) = (3)^(1/4)

The Attempt at a Solution

[sqrt (cot x) = (3)^(1/4)]^4 =

sqrt [cot^2 x = 3] =

cot x = +/- sqrt (3)

x = pi/6, 5pi/6, 7pi/6, 11pi/6

the answer choices to this problem only have two angles each, so two of the angles I derived aren't necessary

 

[Bohrok]

Since the original problem has √(cot x), the solution can't include the values corresponding to cot x = -√3.