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Solving inequalities/ sin4x/3>sqrt(3)/2

sin4x/3>sqrt(3)/2 inequation

A inequation with variable

The solution

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             ___
sin(4*x)   \/ 3 
-------- > -----
   3         2
sin⁡(4x)3>32\frac{\sin{\left(4 x \right)}}{3} > \frac{\sqrt{3}}{2} 
sin(4*x)/3 > sqrt(3)/2
Detail solution
Given the inequality:
sin⁡(4x)3>32\frac{\sin{\left(4 x \right)}}{3} > \frac{\sqrt{3}}{2}
To solve this inequality, we must first solve the corresponding equation:
sin⁡(4x)3=32\frac{\sin{\left(4 x \right)}}{3} = \frac{\sqrt{3}}{2}
Solve:
Given the equation
sin⁡(4x)3=32\frac{\sin{\left(4 x \right)}}{3} = \frac{\sqrt{3}}{2}
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3

The equation is transformed to
sin⁡(4x)=332\sin{\left(4 x \right)} = \frac{3 \sqrt{3}}{2}
As right part of the equation
modulo =
True

but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
x1=π4−asin⁡(332)4x_{1} = \frac{\pi}{4} - \frac{\operatorname{asin}{\left(\frac{3 \sqrt{3}}{2} \right)}}{4}
x2=asin⁡(332)4x_{2} = \frac{\operatorname{asin}{\left(\frac{3 \sqrt{3}}{2} \right)}}{4}
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

sin⁡(0⋅4)3>32\frac{\sin{\left(0 \cdot 4 \right)}}{3} > \frac{\sqrt{3}}{2}
      ___
    \/ 3 
0 > -----
      2

so the inequality has no solutions
Solving inequality on a graph
02468-8-6-4-2-10101-1
Rapid solution
This inequality has no solutions
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