Mister Exam
ctg(x/3-П/6)>0 inequation
The solution
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/x pi\ cot|- - --| > 0 \3 6 /
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0$$
cot(x/3 - pi/6) > 0
Detail solution
Given the inequality:
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} = 0$$
Solve:
$$x_{1} = - \pi$$
$$x_{1} = - \pi$$
This roots
$$x_{1} = - \pi$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \pi - \frac{1}{10}$$
=
$$- \pi - \frac{1}{10}$$
substitute to the expression
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0$$
$$\cot{\left(\frac{- \pi - \frac{1}{10}}{3} - \frac{\pi}{6} \right)} > 0$$
the solution of our inequality is:
$$x < - \pi$$
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} = 0$$
Solve:
$$x_{1} = - \pi$$
$$x_{1} = - \pi$$
This roots
$$x_{1} = - \pi$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \pi - \frac{1}{10}$$
=
$$- \pi - \frac{1}{10}$$
substitute to the expression
$$\cot{\left(\frac{x}{3} - \frac{\pi}{6} \right)} > 0$$
$$\cot{\left(\frac{- \pi - \frac{1}{10}}{3} - \frac{\pi}{6} \right)} > 0$$
tan(1/30) > 0
the solution of our inequality is:
$$x < - \pi$$
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Rapid solution 2
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pi [--, 2*pi) 2
$$x\ in\ \left[\frac{\pi}{2}, 2 \pi\right)$$
x in Interval.Ropen(pi/2, 2*pi)
Rapid solution
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/pi \ And|-- <= x, x < 2*pi| \2 /
$$\frac{\pi}{2} \leq x \wedge x < 2 \pi$$
(pi/2 <= x)∧(x < 2*pi)