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How to use it?
- Inequation:
-
sinx/6>(√3)/2
- log0.5^2(x)+log0.5(x-2)<=0
- x^2*log16(x)>=log16(x)^5+(x)*log2(x)
- 2/log2(2x-2)+3/log2(4x-4)<=8/log3(27)+log2(x-1)
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Identical expressions
- sinx/ six >(√ three)/ two
- sinus of x divide by 6 greater than (√3) divide by 2
- sinus of x divide by six greater than (√ three) divide by two
- sinx/6>√3/2
- sinx divide by 6>(√3) divide by 2
-
Similar expressions
- sin(x/6)>-sqrt(3)/2
- sinx>=√3/2
- sin7x>√3/2
- sin(x/6)>=-2°/2
- sin(x/6)<=-1/2
- cosx>(-√3)/2
- sin(x)<=√3/2
- sin(x/6)>sqrt(3)/2
sinx/6>(√3)/2 inequation
The solution
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___ sin(x) \/ 3 ------ > ----- 6 2
$$\frac{\sin{\left(x \right)}}{6} > \frac{\sqrt{3}}{2}$$
sin(x)/6 > sqrt(3)/2
Detail solution
Given the inequality:
$$\frac{\sin{\left(x \right)}}{6} > \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{6} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{6} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by $\frac{1}{6}$
The equation is transformed to
$$\sin{\left(x \right)} = 3 \sqrt{3}$$
As right part of the equation
modulo =
$$3 \sqrt{3} > 1$$
but sin can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = \pi - \operatorname{asin}{\left(3 \sqrt{3} \right)}$$
$$x_{2} = \operatorname{asin}{\left(3 \sqrt{3} \right)}$$
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
$$x_0 = 0$$
$$\frac{\sin{\left(0 \right)}}{6} > \frac{\sqrt{3}}{2}$$
so the inequality has no solutions
$$\frac{\sin{\left(x \right)}}{6} > \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{6} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{6} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by $\frac{1}{6}$
The equation is transformed to
$$\sin{\left(x \right)} = 3 \sqrt{3}$$
As right part of the equation
modulo =
$$3 \sqrt{3} > 1$$
but sin can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = \pi - \operatorname{asin}{\left(3 \sqrt{3} \right)}$$
$$x_{2} = \operatorname{asin}{\left(3 \sqrt{3} \right)}$$
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
$$x_0 = 0$$
$$\frac{\sin{\left(0 \right)}}{6} > \frac{\sqrt{3}}{2}$$
___
\/ 3
0 > -----
2
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
This inequality has no solutions
The graph