Solve cot (x) - sqrt(3)=0, [0, 2pi)

Answer 1

cot (x) - √3 = 0 so cot (x) = √3

The angle associated with this can be determined by looking at the unit circle:

Since cot = adj/opp, at 30°, it becomes √3/2 divided by 1/2 which is √3. The same holds true for 210° because it's -√3/2 divided by -1/2 which is also √3

In looking at the domain restrictions, it is apparent that the answer should be in radians. 30° and 210° are π/6 and 7π/6 respectively.

You can use your calculator but, since there is no cotangent button you would need to use tan^-1 but then use the reciprocal of √3 which is 1/√3. When you do tan^-1(1/√3) you get 30°. Unfortunately, your calculator can't give you the second value so you MUST consider the unit circle to get this problem correct.

Answer 2

cot x = √3

tan x = √3 / 3

x = π / 6