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)*x^2+32*x+31<=(-2)*x^2+35*x+21
- (x+5)*(x+8)<=0
- 9*bctepiehix+2*6*bctepiehix-3*4*bctepiehix>0
- 10x-27≥15x+13
- Graphing y =:
- tg2x
- Integral of d{x}:
-
tg2x
- Derivative of:
-
tg2x
-
Identical expressions
- tg2x>sqrt three /3
- tg2x greater than square root of 3 divide by 3
- tg2x greater than square root of three divide by 3
- tg2x>√3/3
- tg2x>sqrt3 divide by 3
-
Similar expressions
- tg(x)<=(sqrt(3)/3)
- tg(2x)>=(-1)/sqrt(3)
- arctg^2(x)-4arctgx+3>0
- tg^3x+3>tgx+tg^2x
- cot(x-2*pi/3)>=(-sqrt(3))/3
- tgx>=sqrt(3)/3
- ctg(2x)≤√3
tg2x>sqrt3/3 inequation
The solution
You have entered
[src]
___
\/ 3
tan(2*x) > -----
3
$$\tan{\left(2 x \right)} > \frac{\sqrt{3}}{3}$$
tan(2*x) > sqrt(3)/3
Detail solution
Given the inequality:
$$\tan{\left(2 x \right)} > \frac{\sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(2 x \right)} = \frac{\sqrt{3}}{3}$$
Solve:
Given the equation
$$\tan{\left(2 x \right)} = \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
This roots
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} + \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{12}$$
substitute to the expression
$$\tan{\left(2 x \right)} > \frac{\sqrt{3}}{3}$$
$$\tan{\left(2 \left(\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{12}\right) \right)} > \frac{\sqrt{3}}{3}$$
Then
$$x < \frac{\pi n}{2} + \frac{\pi}{12}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{2} + \frac{\pi}{12}$$
$$\tan{\left(2 x \right)} > \frac{\sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(2 x \right)} = \frac{\sqrt{3}}{3}$$
Solve:
Given the equation
$$\tan{\left(2 x \right)} = \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
This roots
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} + \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{12}$$
substitute to the expression
$$\tan{\left(2 x \right)} > \frac{\sqrt{3}}{3}$$
$$\tan{\left(2 \left(\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{12}\right) \right)} > \frac{\sqrt{3}}{3}$$
___
/ 1 pi \ \/ 3
tan|- - + -- + pi*n| > -----
\ 5 6 / 3
Then
$$x < \frac{\pi n}{2} + \frac{\pi}{12}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{2} + \frac{\pi}{12}$$
_____
/
-------ο-------
x1
Solving inequality on a graph
Rapid solution 2
[src]
/ ___ ___\
|\/ 2 - \/ 6 | pi
(-atan|-------------|, --)
| ___ ___| 4
\\/ 2 + \/ 6 /
$$x\ in\ \left(- \operatorname{atan}{\left(\frac{- \sqrt{6} + \sqrt{2}}{\sqrt{2} + \sqrt{6}} \right)}, \frac{\pi}{4}\right)$$
x in Interval.open(-atan((-sqrt(6) + sqrt(2))/(sqrt(2) + sqrt(6))), pi/4)
Rapid solution
[src]
/ / ___ ___\ \ | pi |\/ 2 - \/ 6 | | And|x < --, -atan|-------------| < x| | 4 | ___ ___| | \ \\/ 2 + \/ 6 / /
$$x < \frac{\pi}{4} \wedge - \operatorname{atan}{\left(\frac{- \sqrt{6} + \sqrt{2}}{\sqrt{2} + \sqrt{6}} \right)} < x$$
(x < pi/4)∧(-atan((sqrt(2) - sqrt(6))/(sqrt(2) + sqrt(6))) < x)