Trigonometric inequalities: |cot(x)| <= sqrt(3)

[yeunju]

This is the problem:
|cot(x)| ? ?3
(absolute value of cotangent x is less than or equal to square root of 3)

I've looked up some examples online and it said to isolate the terms, in this case cot(x)

So i made cot(x) = ?3 just to keep it simple, leaving the inequality sign out. Then, I realized that a graph would help out so i graphed cot(x) in my graphing calculator in radian mode. Shows zeros at ?/2 and 3?/2 with some lines going above the x-axis and some under.

My problem was how the root three would make my answer different~ I know cot(x)= cos(x)/sin(x)= 1/tan(x) but i dont know how to relate it to the root 3? And..I dont know how my answer is supposed to look like? radians? inequalities.

 

[JRH]

It kind of looks like the Eiffel Tower with the y-axis going straight up the middle, except that it stops on the positive side of the x-axis at sqrt(3), it would of course continue on to negative infinity with complete Eiffel Towers all the way down with a frequency of pi.

 

[JRH]

I take that back, with the absolute value there, it just looks like one Eiffel Tower with the y-axis going up the middle as before -sqrt(3) and after sqrt(3) there is nothing.