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Solving inequalities/ sinx/4<-sqrt(3)/2

sinx/4<-sqrt(3)/2 inequation

A inequation with variable

The solution

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

The equation is transformed to
sin⁡(x)=−23\sin{\left(x \right)} = - 2 \sqrt{3}
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=π+asin⁡(23)x_{1} = \pi + \operatorname{asin}{\left(2 \sqrt{3} \right)}
x2=−asin⁡(23)x_{2} = - \operatorname{asin}{\left(2 \sqrt{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

sin⁡(0)4<(−1)32\frac{\sin{\left(0 \right)}}{4} < \frac{\left(-1\right) \sqrt{3}}{2}
       ___ 
    -\/ 3  
0 < -------
       2

but
       ___ 
    -\/ 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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