Mister Exam
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- Square Inequality Step-by-Step
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- Logarithmic inequality online
-
How to use it?
- Inequation:
- ab(a+b)+bc(b+c)+ac(a+c)>=6abc
- 2x²-9x+7<0
- (x-2):(4-x)>=0
- log(2-x)<2*log(4)-log(2)
- Derivative of:
-
cosx/3
- Graphing y =:
-
cosx/3
- Integral of d{x}:
- cosx/3
-
Identical expressions
- cosx/ three <√ three / two
- co sinus of e of x divide by 3 less than √3 divide by 2
- co sinus of e of x divide by three less than √ three divide by two
- cosx divide by 3<√3 divide by 2
-
Similar expressions
- cos(x)/3>0
- cos(x/3)<=sqrt(3)/2
- cos(x/3+p/3)<√2/2
cosx/3<√3/2 inequation
The solution
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[src]
___ cos(x) \/ 3 ------ < ----- 3 2
$$\frac{\cos{\left(x \right)}}{3} < \frac{\sqrt{3}}{2}$$
cos(x)/3 < sqrt(3)/2
Detail solution
Given the inequality:
$$\frac{\cos{\left(x \right)}}{3} < \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\cos{\left(x \right)}}{3} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\cos{\left(x \right)}}{3} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = \frac{3 \sqrt{3}}{2}$$
As right part of the equation
modulo =
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(\frac{3 \sqrt{3}}{2} \right)}$$
$$x_{2} = \operatorname{acos}{\left(\frac{3 \sqrt{3}}{2} \right)}$$
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
$$\frac{\cos{\left(0 \right)}}{3} < \frac{\sqrt{3}}{2}$$
so the inequality is always executed
$$\frac{\cos{\left(x \right)}}{3} < \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\cos{\left(x \right)}}{3} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\frac{\cos{\left(x \right)}}{3} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3
The equation is transformed to
$$\cos{\left(x \right)} = \frac{3 \sqrt{3}}{2}$$
As right part of the equation
modulo =
True
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(\frac{3 \sqrt{3}}{2} \right)}$$
$$x_{2} = \operatorname{acos}{\left(\frac{3 \sqrt{3}}{2} \right)}$$
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
$$\frac{\cos{\left(0 \right)}}{3} < \frac{\sqrt{3}}{2}$$
___
\/ 3
1/3 < -----
2
so the inequality is always executed
Solving inequality on a graph