Mister Exam
(tg(2*x))*(1/(sqrt(3)))>1/sqrt(3) inequation
The solution
You have entered
[src]
tan(2*x) 1 -------- > ----- ___ ___ \/ 3 \/ 3
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
tan(2*x)/sqrt(3) > 1/(sqrt(3))
Detail solution
Given the inequality:
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} = \frac{1}{\sqrt{3}}$$
Solve:
Given the equation
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} = \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(2 x \right)} = 1$$
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
This roots
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} + \frac{\pi}{8}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{8}$$
substitute to the expression
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
$$\frac{\tan{\left(2 \left(\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{8}\right) \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
Then
$$x < \frac{\pi n}{2} + \frac{\pi}{8}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{2} + \frac{\pi}{8}$$
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} = \frac{1}{\sqrt{3}}$$
Solve:
Given the equation
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} = \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by sqrt(3)/3
The equation is transformed to
$$\tan{\left(2 x \right)} = 1$$
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
This roots
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} + \frac{\pi}{8}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{8}$$
substitute to the expression
$$\frac{\tan{\left(2 x \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
$$\frac{\tan{\left(2 \left(\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{8}\right) \right)}}{\sqrt{3}} > \frac{1}{\sqrt{3}}$$
___ / 1 pi \ ___
\/ 3 *tan|- - + -- + pi*n| \/ 3
\ 5 4 / > -----
-------------------------- 3
3 Then
$$x < \frac{\pi n}{2} + \frac{\pi}{8}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{2} + \frac{\pi}{8}$$
_____
/
-------ο-------
x1
Solving inequality on a graph