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tgx>(-cbrt(3)/cbrt(3)) inequation

A inequation with variable

The solution

You have entered [src]
          3 ___ 
         -\/ 3  
tan(x) > -------
          3 ___ 
          \/ 3  
$$\tan{\left(x \right)} > \frac{\left(-1\right) \sqrt[3]{3}}{\sqrt[3]{3}}$$
tan(x) > (-3^(1/3))/3^(1/3)
Detail solution
Given the inequality:
$$\tan{\left(x \right)} > \frac{\left(-1\right) \sqrt[3]{3}}{\sqrt[3]{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = \frac{\left(-1\right) \sqrt[3]{3}}{\sqrt[3]{3}}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = \frac{\left(-1\right) \sqrt[3]{3}}{\sqrt[3]{3}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{1} = \pi n - \frac{\pi}{4}$$
This roots
$$x_{1} = \pi n - \frac{\pi}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{4}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{4} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} > \frac{\left(-1\right) \sqrt[3]{3}}{\sqrt[3]{3}}$$
$$\tan{\left(\pi n - \frac{\pi}{4} - \frac{1}{10} \right)} > \frac{\left(-1\right) \sqrt[3]{3}}{\sqrt[3]{3}}$$
    /1    pi       \     
-tan|-- + -- - pi*n| > -1
    \10   4        /     

Then
$$x < \pi n - \frac{\pi}{4}$$
no execute
the solution of our inequality is:
$$x > \pi n - \frac{\pi}{4}$$
         _____  
        /
-------ο-------
       x1
Solving inequality on a graph
Rapid solution [src]
  /   /            pi\     /         3*pi    \\
Or|And|0 <= x, x < --|, And|x <= pi, ---- < x||
  \   \            2 /     \          4      //
$$\left(0 \leq x \wedge x < \frac{\pi}{2}\right) \vee \left(x \leq \pi \wedge \frac{3 \pi}{4} < x\right)$$
((0 <= x)∧(x < pi/2))∨((x <= pi)∧(3*pi/4 < x))
Rapid solution 2 [src]
    pi     3*pi     
[0, --) U (----, pi]
    2       4       
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left(\frac{3 \pi}{4}, \pi\right]$$
x in Union(Interval.Ropen(0, pi/2), Interval.Lopen(3*pi/4, pi))