Mister Exam
2cosx/2>-√3 inequation
The solution
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2*cos(x) ___ -------- > -\/ 3 2
$$\frac{2 \cos{\left(x \right)}}{2} > - \sqrt{3}$$
(2*cos(x))/2 > -sqrt(3)
Detail solution
Given the inequality:
$$\frac{2 \cos{\left(x \right)}}{2} > - \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 \cos{\left(x \right)}}{2} = - \sqrt{3}$$
Solve:
Given the equation
$$\frac{2 \cos{\left(x \right)}}{2} = - \sqrt{3}$$
- this is the simplest trigonometric equation
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.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(- \sqrt{3} \right)}$$
$$x_{2} = \operatorname{acos}{\left(- \sqrt{3} \right)}$$
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
$$\frac{2 \cos{\left(0 \right)}}{2} > - \sqrt{3}$$
so the inequality is always executed
$$\frac{2 \cos{\left(x \right)}}{2} > - \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 \cos{\left(x \right)}}{2} = - \sqrt{3}$$
Solve:
Given the equation
$$\frac{2 \cos{\left(x \right)}}{2} = - \sqrt{3}$$
- this is the simplest trigonometric equation
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.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(- \sqrt{3} \right)}$$
$$x_{2} = \operatorname{acos}{\left(- \sqrt{3} \right)}$$
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
$$\frac{2 \cos{\left(0 \right)}}{2} > - \sqrt{3}$$
___
1 > -\/ 3
so the inequality is always executed
Solving inequality on a graph