Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- -6*x^2+13*x-5>=0
- |x-1|-(6/|x-1|)<1
- 6x-7<8x-9
-
tg(pi-x)<1/sqrt3
-
Identical expressions
- tg(pi-x)< one /sqrt3
- tg( Pi minus x) less than 1 divide by square root of 3
- tg( Pi minus x) less than one divide by square root of 3
- tg(pi-x)<1/√3
- tgpi-x<1/sqrt3
- tg(pi-x)<1 divide by sqrt3
-
Similar expressions
- tan(x+pi/6)>1/(sqrt(3))
- tg(pi+x)<1/sqrt3
- (tg(2*x))*(1/(sqrt(3)))>1/sqrt(3)
- tan(x)+cot(x)>=1/(sqrt(3))+sqrt(3)
- tan(5*x-pi/3)>=(-1)/sqrt(3)
tg(pi-x)<1/sqrt3 inequation
The solution
You have entered
[src]
1
tan(pi - x) < 1*-----
___
\/ 3
$$\tan{\left(\pi - x \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
tan(pi - x) < 1/sqrt(3)
Detail solution
Given the inequality:
$$\tan{\left(\pi - x \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(\pi - x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
Solve:
Given the equation
$$\tan{\left(\pi - x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = - \frac{\sqrt{3}}{3}$$
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:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{6}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{6} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(\pi - x \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
$$\tan{\left(\pi - \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
but
Then
$$x < \pi n - \frac{\pi}{6}$$
no execute
the solution of our inequality is:
$$x > \pi n - \frac{\pi}{6}$$
$$\tan{\left(\pi - x \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(\pi - x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
Solve:
Given the equation
$$\tan{\left(\pi - x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\tan{\left(x \right)} = - \frac{\sqrt{3}}{3}$$
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:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{6}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{6} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(\pi - x \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
$$\tan{\left(\pi - \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} < 1 \cdot \frac{1}{\sqrt{3}}$$
___
/1 pi\ \/ 3
tan|-- + --| < -----
\10 6 / 3
but
___
/1 pi\ \/ 3
tan|-- + --| > -----
\10 6 / 3
Then
$$x < \pi n - \frac{\pi}{6}$$
no execute
the solution of our inequality is:
$$x > \pi n - \frac{\pi}{6}$$
_____
/
-------ο-------
x_1
Solving inequality on a graph
Rapid solution 2
[src]
pi 5*pi
[0, --) U (----, pi)
2 6
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left(\frac{5 \pi}{6}, \pi\right)$$
x in Union(Interval.Ropen(0, pi/2), Interval.open(5*pi/6, pi))
Rapid solution
[src]
/ / pi\ /5*pi \\ Or|And|0 <= x, x < --|, And|---- < x, x < pi|| \ \ 2 / \ 6 //
$$\left(0 \leq x \wedge x < \frac{\pi}{2}\right) \vee \left(\frac{5 \pi}{6} < x \wedge x < \pi\right)$$
((0 <= x)∧(x < pi/2))∨((x < pi)∧(5*pi/6 < x))
The graph