Trig Inequalities: Solve tanx - 3cotx = 0 in the Interval [0, 2pi)

[zeion]

Homework Statement

Solve the following equations or inequalities in the interval [0, 2pi)

tanx - 3cotx = 0

Homework Equations

The Attempt at a Solution

tanx = 3cotx
tanx = 3/tanx
tan²x = 3
tanx = +-sqrt3
tanx = sqrt3 or tanx = -sqrt3

tanx = sqrt3
x = pi/3, 7pi/6

tanx = -sqrt3
x = 2pi/3, 11pi/6

Is this right?

 

[lanedance]

check your answers

tan is periodic with a period of pi, your solutions for a given sign do not have period of pi

 

[mrkuo]

Both your primary answers to each equation were correct.

But why did you from answers with reference angles of pi/3 to that of pi/6 for your secondary answers?