math problem I do not get this

Question

Consider the equation 3−cot²x=0 . Find all the values of x in the interval [0,2π] that satisfy the equation.

Note: Write the exact answer but not the approximate value (For example write 4/5 but not 0.8). Also write Pi or pi or π if there is a π in the answer.

1.Write the value of x in the interval [0,π/2] that satisfy the equation.

1. Write the value of x in the interval [π/2,π] that satisfy the equation.

help please me I don't get this

Answer 1

3-cot^2(x) = 0

cot^2(x) = 3

cot(x) = + or - sqr3

cotangent of an angle = adjacent side over the opposite side

sqr3 = sqr3/1 where sqr3 = adjacent side and 1 = the opposite side

that's a familiar 30-60-90 right triangle with sides in the ratio of 1 - sqr3 - 2

x = 30, 330, 150 or 210 degrees

but only 30 is in the interval 0 to pi/2

or

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

only x=pi/6 in the interval 0 to pi/2

for the interval pi/2 to pi

x = 150 degrees or 5pi/6

if you aren't familiar with the familiar right triangle 30-60-90

use a calculator with an inverse cotangent function. punch in sqr3, then take the inverse cotangent function to get either 30 degrees or pi/6

for the interval pi/2 to pi

subtract: pi-pi/6 = 5pi/6 which equals 150 degrees