Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- log2(1-x)>log2(2x-8)
- y^2-4*x+8>0
- 4x−3x**2−9≤0
- (x-4)^2>16-x^2
- Integral of d{x}:
-
sinx/2
- Derivative of:
-
sinx/2
- -√3/2
- Graphing y =:
-
sinx/2
-
Identical expressions
- sinx/ two <-√ three / two
- sinus of x divide by 2 less than minus √3 divide by 2
- sinus of x divide by two less than minus √ three divide by two
- sinx divide by 2<-√3 divide by 2
-
Similar expressions
- sin<=-(√3)/2
- cos(2x-(pi/4))x≤-(√3/2)
- sin(x/2)>=sqrt-3/2
- cosx<=-(√3/2)
- 2*sin(x/2-pi/4)>1
- sinx/2<+√3/2
- sin(x/2)<1
sinx/2<-√3/2 inequation
The solution
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___ sin(x) -\/ 3 ------ < ------- 2 2
$$\frac{\sin{\left(x \right)}}{2} < \frac{\left(-1\right) \sqrt{3}}{2}$$
sin(x)/2 < (-sqrt(3))/2
Detail solution
Given the inequality:
$$\frac{\sin{\left(x \right)}}{2} < \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{2} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{2} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = - \sqrt{3}$$
As right part of the equation
modulo =
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = \pi + \operatorname{asin}{\left(\sqrt{3} \right)}$$
$$x_{2} = - \operatorname{asin}{\left(\sqrt{3} \right)}$$
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
$$\frac{\sin{\left(0 \right)}}{2} < \frac{\left(-1\right) \sqrt{3}}{2}$$
but
so the inequality has no solutions
$$\frac{\sin{\left(x \right)}}{2} < \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{2} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{2} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/2
The equation is transformed to
$$\sin{\left(x \right)} = - \sqrt{3}$$
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.
$$x_{1} = \pi + \operatorname{asin}{\left(\sqrt{3} \right)}$$
$$x_{2} = - \operatorname{asin}{\left(\sqrt{3} \right)}$$
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
$$\frac{\sin{\left(0 \right)}}{2} < \frac{\left(-1\right) \sqrt{3}}{2}$$
___
-\/ 3
0 < -------
2
but
___
-\/ 3
0 > -------
2
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
This inequality has no solutions