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cos(x)>(-2)/sqrt(3) inequation

A inequation with variable

The solution

You have entered [src]
          -2  
cos(x) > -----
           ___
         \/ 3 
$$\cos{\left(x \right)} > - \frac{2}{\sqrt{3}}$$
cos(x) > -2*sqrt(3)/3
Detail solution
Given the inequality:
$$\cos{\left(x \right)} > - \frac{2}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(x \right)} = - \frac{2}{\sqrt{3}}$$
Solve:
Given the equation
$$\cos{\left(x \right)} = - \frac{2}{\sqrt{3}}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
True

but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(- \frac{2 \sqrt{3}}{3} \right)}$$
$$x_{2} = \operatorname{acos}{\left(- \frac{2 \sqrt{3}}{3} \right)}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0

$$\cos{\left(0 \right)} > - \frac{2}{\sqrt{3}}$$
         ___
    -2*\/ 3 
1 > --------
       3    
    

so the inequality is always executed
Solving inequality on a graph
Rapid solution 2 [src]
(-oo, oo)
$$x\ in\ \left(-\infty, \infty\right)$$
x in Interval(-oo, oo)
Rapid solution [src]
And(-oo < x, x < oo)
$$-\infty < x \wedge x < \infty$$
(-oo < x)∧(x < oo)