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Solving inequalities/ ctg(x/3-П/6)>0

ctg(x/3-П/6)>0 inequation

A inequation with variable

The solution

You have entered [src] 
   /x   pi\    
cot|- - --| > 0
   \3   6 /
cot⁡(x3−π6)>0\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0 
cot(x/3 - pi/6) > 0
Detail solution
Given the inequality:
cot⁡(x3−π6)>0\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0
To solve this inequality, we must first solve the corresponding equation:
cot⁡(x3−π6)=0\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} = 0
Solve:
x1=−πx_{1} = - \pi
x1=−πx_{1} = - \pi
This roots
x1=−πx_{1} = - \pi
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1−110x_{0} = x_{1} - \frac{1}{10}
=
−π−110- \pi - \frac{1}{10}
=
−π−110- \pi - \frac{1}{10}
substitute to the expression
cot⁡(x3−π6)>0\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0
cot⁡(−π−1103−π6)>0\cot{\left(\frac{- \pi - \frac{1}{10}}{3} - \frac{\pi}{6} \right)} > 0
tan(1/30) > 0

the solution of our inequality is:
x<−πx < - \pi
 _____          
      \    
-------ο-------
       x1
Rapid solution 2 [src] 
 pi       
[--, 2*pi)
 2
x in [π2,2π)x\ in\ \left[\frac{\pi}{2}, 2 \pi\right) 
x in Interval.Ropen(pi/2, 2*pi)
Rapid solution [src] 
   /pi               \
And|-- <= x, x < 2*pi|
   \2                /
π2≤x∧x<2π\frac{\pi}{2} \leq x \wedge x < 2 \pi 
(pi/2 <= x)∧(x < 2*pi)
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