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How to use it?
- Inequation:
- 4(x-5)>=3/(x+2)
- (x^2+3^x-3)^5>(x^2+9^x-3^x)*5
- 16^x-9<1
- |4x-3|≥2x+3
-
Identical expressions
- sin4x/ three >-sqrt(three)/ two
- sinus of 4x divide by 3 greater than minus square root of (3) divide by 2
- sinus of 4x divide by three greater than minus square root of (three) divide by two
- sin4x/3>-√(3)/2
- sin4x/3>-sqrt3/2
- sin4x divide by 3>-sqrt(3) divide by 2
-
Similar expressions
- sin(4*x)/3>=sqrt(3)/2
- sin((4*x)/3)>-sqrt(3)*1/2
- sin4x/3>+sqrt(3)/2
- cos>=-sqrt3/2
- sin(4*x/3)>-(sqrt(3)/2)
- cos(x/2)>=-sqrt3/2
- sin(x)>=(-sqrt(3))/2
- cosx>=-sqrt3/2
sin4x/3>-sqrt(3)/2 inequation
The solution
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[src]
___ sin(4*x) -\/ 3 -------- > ------- 3 2
$$\frac{\sin{\left(4 x \right)}}{3} > \frac{\left(-1\right) \sqrt{3}}{2}$$
sin(4*x)/3 > -sqrt(3)/2
Detail solution
Given the inequality:
$$\frac{\sin{\left(4 x \right)}}{3} > \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(4 x \right)}}{3} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(4 x \right)}}{3} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(4 x \right)} = - \frac{3 \sqrt{3}}{2}$$
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.
$$x_{1} = \frac{\pi}{4} + \frac{\operatorname{asin}{\left(\frac{3 \sqrt{3}}{2} \right)}}{4}$$
$$x_{2} = - \frac{\operatorname{asin}{\left(\frac{3 \sqrt{3}}{2} \right)}}{4}$$
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
$$\frac{\sin{\left(4 \cdot 0 \right)}}{3} > \frac{\left(-1\right) \sqrt{3}}{2}$$
so the inequality is always executed
$$\frac{\sin{\left(4 x \right)}}{3} > \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(4 x \right)}}{3} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(4 x \right)}}{3} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3
The equation is transformed to
$$\sin{\left(4 x \right)} = - \frac{3 \sqrt{3}}{2}$$
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.
$$x_{1} = \frac{\pi}{4} + \frac{\operatorname{asin}{\left(\frac{3 \sqrt{3}}{2} \right)}}{4}$$
$$x_{2} = - \frac{\operatorname{asin}{\left(\frac{3 \sqrt{3}}{2} \right)}}{4}$$
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
$$\frac{\sin{\left(4 \cdot 0 \right)}}{3} > \frac{\left(-1\right) \sqrt{3}}{2}$$
___
-\/ 3
0 > -------
2
so the inequality is always executed
Solving inequality on a graph
The graph