Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 14logax+19/logax^2+4<1
- −(3x+2)+(x−7)>0
- 2log_2^2(x)-3log_2(x)+2<=0
- (5/(sqrtx-1)-5)>=-1
- Derivative of:
-
sin(x)/4
- Integral of d{x}:
- sin(x)/4
-
Identical expressions
- sin(x)/ four <-(three)^(one / two)/ two
- sinus of (x) divide by 4 less than minus (3) to the power of (1 divide by 2) divide by 2
- sinus of (x) divide by four less than minus (three) to the power of (one divide by two) divide by two
- sin(x)/4<-(3)(1/2)/2
- sinx/4<-31/2/2
- sinx/4<-3^1/2/2
- sin(x) divide by 4<-(3)^(1 divide by 2) divide by 2
-
Similar expressions
- sin(x/4+2)<(-sqrt(2))/2
- sin(x/4)<-sqrt3/2
- sin(x/4)<sqrt-(3/2)
- sin(x)/4<+(3)^(1/2)/2
- (sinx/4+cosx/4)²≤1/2
- sinx/4<-(3)^(1/2)/2
sin(x)/4<-(3)^(1/2)/2 inequation
The solution
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[src]
___ sin(x) -\/ 3 ------ < ------- 4 2
$$\frac{\sin{\left(x \right)}}{4} < \frac{\left(-1\right) \sqrt{3}}{2}$$
sin(x)/4 < (-sqrt(3))/2
Detail solution
Given the inequality:
$$\frac{\sin{\left(x \right)}}{4} < \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = - 2 \sqrt{3}$$
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.
$$x_{1} = \pi + \operatorname{asin}{\left(2 \sqrt{3} \right)}$$
$$x_{2} = - \operatorname{asin}{\left(2 \sqrt{3} \right)}$$
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
$$\frac{\sin{\left(0 \right)}}{4} < \frac{\left(-1\right) \sqrt{3}}{2}$$
but
so the inequality has no solutions
$$\frac{\sin{\left(x \right)}}{4} < \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/4
The equation is transformed to
$$\sin{\left(x \right)} = - 2 \sqrt{3}$$
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.
$$x_{1} = \pi + \operatorname{asin}{\left(2 \sqrt{3} \right)}$$
$$x_{2} = - \operatorname{asin}{\left(2 \sqrt{3} \right)}$$
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
$$\frac{\sin{\left(0 \right)}}{4} < \frac{\left(-1\right) \sqrt{3}}{2}$$
___
-\/ 3
0 < -------
2
but
___
-\/ 3
0 > -------
2
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
This inequality has no solutions