Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
3-4x>=11
-
tgx<=1/sqrt(3)
- ctg(x)<=-1
- log(0.5,x^2-4x+3)>=-3
- Integral of d{x}:
-
tgx
- Derivative of:
-
tgx
- Graphing y =:
-
tgx
-
Identical expressions
- tgx<= one /sqrt(three)
- tgx less than or equal to 1 divide by square root of (3)
- tgx less than or equal to one divide by square root of (three)
- tgx<=1/√(3)
- tgx<=1/sqrt3
- tgx<=1 divide by sqrt(3)
-
Similar expressions
- ctg(x)<-sqrt(3)
- ctg(x)<=-1
- ctg(x/3+pi/6)>-sqrt(3)/3
- ctg(x/2)=>1+ctg(x)
tgx<=1/sqrt(3) inequation
The solution
You have entered
[src]
1
tan(x) <= 1*-----
___
\/ 3
$$\tan{\left(x \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
tan(x) <= 1/sqrt(3)
Detail solution
Given the inequality:
$$\tan{\left(x \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{6}$$
, where n - is a integer
$$x_{1} = \pi n + \frac{\pi}{6}$$
$$x_{1} = \pi n + \frac{\pi}{6}$$
This roots
$$x_{1} = \pi n + \frac{\pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \frac{\pi}{6}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \frac{\pi}{6}$$
substitute to the expression
$$\tan{\left(x \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
$$\tan{\left(\pi n - \frac{1}{10} + \frac{\pi}{6} \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
the solution of our inequality is:
$$x \leq \pi n + \frac{\pi}{6}$$
$$\tan{\left(x \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{6}$$
, where n - is a integer
$$x_{1} = \pi n + \frac{\pi}{6}$$
$$x_{1} = \pi n + \frac{\pi}{6}$$
This roots
$$x_{1} = \pi n + \frac{\pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \frac{\pi}{6}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \frac{\pi}{6}$$
substitute to the expression
$$\tan{\left(x \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
$$\tan{\left(\pi n - \frac{1}{10} + \frac{\pi}{6} \right)} \leq 1 \cdot \frac{1}{\sqrt{3}}$$
___
/1 pi\ \/ 3
cot|-- + --| <= -----
\10 3 / 3
the solution of our inequality is:
$$x \leq \pi n + \frac{\pi}{6}$$
_____
\
-------•-------
x_1
Solving inequality on a graph
Rapid solution
[src]
/ / pi\ /pi \\ Or|And|0 <= x, x <= --|, And|-- < x, x < pi|| \ \ 6 / \2 //
$$\left(0 \leq x \wedge x \leq \frac{\pi}{6}\right) \vee \left(\frac{\pi}{2} < x \wedge x < \pi\right)$$
((0 <= x)∧(x <= pi/6))∨((x < pi)∧(pi/2 < x))
Rapid solution 2
[src]
pi pi
[0, --] U (--, pi)
6 2
$$x\ in\ \left[0, \frac{\pi}{6}\right] \cup \left(\frac{\pi}{2}, \pi\right)$$
x in Union(Interval(0, pi/6), Interval.open(pi/2, pi))
The graph