Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
ctgx>=sqrt(3)/3
- cos(x)+sqrt(2)*cos(2*x)+sin(x)>=0
- 3x<-3
- 3x²+2x-5<=0
- Integral of d{x}:
- ctgx
- Derivative of:
-
ctgx
-
Identical expressions
- ctgx>=sqrt(three)/ three
- ctgx greater than or equal to square root of (3) divide by 3
- ctgx greater than or equal to square root of (three) divide by three
- ctgx>=√(3)/3
- ctgx>=sqrt3/3
- ctgx>=sqrt(3) divide by 3
-
Similar expressions
- ctg(x)<-sqrt(3)
ctgx>=sqrt(3)/3 inequation
The solution
You have entered
[src]
___
\/ 3
cot(x) >= -----
3
$$\cot{\left(x \right)} \geq \frac{\sqrt{3}}{3}$$
cot(x) >= sqrt(3)/3
Detail solution
Given the inequality:
$$\cot{\left(x \right)} \geq \frac{\sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x \right)} = \frac{\sqrt{3}}{3}$$
Solve:
Given the equation
$$\cot{\left(x \right)} = \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acot}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
$$x_{1} = \pi n + \frac{\pi}{3}$$
$$x_{1} = \pi n + \frac{\pi}{3}$$
This roots
$$x_{1} = \pi n + \frac{\pi}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \frac{\pi}{3}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \frac{\pi}{3}$$
substitute to the expression
$$\cot{\left(x \right)} \geq \frac{\sqrt{3}}{3}$$
$$\cot{\left(\pi n - \frac{1}{10} + \frac{\pi}{3} \right)} \geq \frac{\sqrt{3}}{3}$$
the solution of our inequality is:
$$x \leq \pi n + \frac{\pi}{3}$$
$$\cot{\left(x \right)} \geq \frac{\sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x \right)} = \frac{\sqrt{3}}{3}$$
Solve:
Given the equation
$$\cot{\left(x \right)} = \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acot}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
$$x_{1} = \pi n + \frac{\pi}{3}$$
$$x_{1} = \pi n + \frac{\pi}{3}$$
This roots
$$x_{1} = \pi n + \frac{\pi}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \frac{\pi}{3}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \frac{\pi}{3}$$
substitute to the expression
$$\cot{\left(x \right)} \geq \frac{\sqrt{3}}{3}$$
$$\cot{\left(\pi n - \frac{1}{10} + \frac{\pi}{3} \right)} \geq \frac{\sqrt{3}}{3}$$
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/1 pi\ \/ 3
tan|-- + --| >= -----
\10 6 / 3
the solution of our inequality is:
$$x \leq \pi n + \frac{\pi}{3}$$
_____
\
-------•-------
x_1
Solving inequality on a graph
Rapid solution 2
[src]
pi
(0, --]
3
$$x\ in\ \left(0, \frac{\pi}{3}\right]$$
x in Interval.Lopen(0, pi/3)
Rapid solution
[src]
/ pi \ And|x <= --, 0 < x| \ 3 /
$$x \leq \frac{\pi}{3} \wedge 0 < x$$
(0 < x)∧(x <= pi/3)
The graph