Mister Exam
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- Square Inequality Step-by-Step
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-
How to use it?
- Inequation:
- (|x|)+(|x-3|)>=3
- 4x-3(5x+8)<_-7
- 4^x<=8^(sqrtx+sqrt1)
- 5x+25<=2x-2
- Integral of d{x}:
-
sinx/2
- Derivative of:
-
sinx/2
- Graphing y =:
-
sinx/2
-
Identical expressions
- sinx/ two <√ three / two
- sinus of x divide by 2 less than √3 divide by 2
- sinus of x divide by two less than √ three divide by two
- sinx divide by 2<√3 divide by 2
-
Similar expressions
- sin<=-(√3)/2
- 2sin(x/2+pi/4)<=cbrt(2)
- cos(x/2)^2-sin(x/2)^2<0
- log(2)*sin((x)/(2))<-1
sinx/2<√3/2 inequation
The solution
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___ sin(x) \/ 3 ------ < ----- 2 2
$$\frac{\sin{\left(x \right)}}{2} < \frac{\sqrt{3}}{2}$$
sin(x)/2 < sqrt(3)/2
Detail solution
Given the inequality:
$$\frac{\sin{\left(x \right)}}{2} < \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
- 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
$$\frac{\sin{\left(0 \right)}}{2} < \frac{\sqrt{3}}{2}$$
so the inequality is always executed
$$\frac{\sin{\left(x \right)}}{2} < \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
- 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
$$\frac{\sin{\left(0 \right)}}{2} < \frac{\sqrt{3}}{2}$$
___
\/ 3
0 < -----
2
so the inequality is always executed
Solving inequality on a graph