Mister Exam
cot(7*x+(2*pi/3))>-sqrt(3)/3 inequation
The solution
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___ / 2*pi\ -\/ 3 cot|7*x + ----| > ------- \ 3 / 3
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
cot(7*x + (2*pi)/3) > (-sqrt(3))/3
Detail solution
Given the inequality:
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solve:
$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
$$\cot{\left(\frac{\left(-1\right) 7}{10} + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
the solution of our inequality is:
$$x < 0$$
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solve:
$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$\cot{\left(7 x + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
$$\cot{\left(\frac{\left(-1\right) 7}{10} + \frac{2 \pi}{3} \right)} > \frac{\left(-1\right) \sqrt{3}}{3}$$
___
/7 pi\ -\/ 3
-cot|-- + --| > -------
\10 3 / 3
the solution of our inequality is:
$$x < 0$$
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