Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- (|x|)+(|x-3|)>=3
- √(x^2-2x)>4-x
- 3^(x+2)>81
- (x^2+5*x)/(x-6)>0
- Graphing y =:
- tg2x
- Integral of d{x}:
-
tg2x
- Derivative of:
-
tg2x
-
Identical expressions
- tg2x<(-sqrt three /3)
- tg2x less than ( minus square root of 3 divide by 3)
- tg2x less than ( minus square root of three divide by 3)
- tg2x<(-√3/3)
- tg2x<-sqrt3/3
- tg2x<(-sqrt3 divide by 3)
-
Similar expressions
- ctg(2x)<=1
- tgx>(-sqrt(3)/3)
- (x^2-99x-100)log0,2(tg^2x)<(99x+100-x^2)th(tgx-6)
- arctg^2(x)/n^3<=1/n^3
- ctg(x)>=(-sqrt(3))/3
- tan(-pi*1/3+5*x)>=-sqrt(3)/3
- ctg(2x)≤√3
- tg2x<(sqrt3/3)
- cot(1/2*x-pi/4)<=-sqrt(3)/3
tg2x<(-sqrt3/3) inequation
The solution
You have entered
[src]
___
-\/ 3
tan(2*x) < -------
3
$$\tan{\left(2 x \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
tan(2*x) < (-sqrt(3))/3
Detail solution
Given the inequality:
$$\tan{\left(2 x \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solve:
Given the equation
$$\tan{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- 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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} - \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{\pi}{12} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(2 x \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
$$\tan{\left(2 \left(\frac{\pi n}{2} - \frac{\pi}{12} - \frac{1}{10}\right) \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
the solution of our inequality is:
$$x < \frac{\pi n}{2} - \frac{\pi}{12}$$
$$\tan{\left(2 x \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solve:
Given the equation
$$\tan{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- 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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} - \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{\pi}{12} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(2 x \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
$$\tan{\left(2 \left(\frac{\pi n}{2} - \frac{\pi}{12} - \frac{1}{10}\right) \right)} < \frac{\left(-1\right) \sqrt{3}}{3}$$
___
/1 pi \ -\/ 3
-tan|- + -- - pi*n| < -------
\5 6 / 3
the solution of our inequality is:
$$x < \frac{\pi n}{2} - \frac{\pi}{12}$$
_____
\
-------ο-------
x1
Solving inequality on a graph
Rapid solution
[src]
/ / ___ ___\\ |pi |\/ 2 + \/ 6 || And|-- < x, x < -atan|-------------|| |4 | ___ ___|| \ \\/ 2 - \/ 6 //
$$\frac{\pi}{4} < x \wedge x < - \operatorname{atan}{\left(\frac{\sqrt{2} + \sqrt{6}}{- \sqrt{6} + \sqrt{2}} \right)}$$
(pi/4 < x)∧(x < -atan((sqrt(2) + sqrt(6))/(sqrt(2) - sqrt(6))))
Rapid solution 2
[src]
/ ___ ___\
pi |\/ 2 + \/ 6 |
(--, -atan|-------------|)
4 | ___ ___|
\\/ 2 - \/ 6 /
$$x\ in\ \left(\frac{\pi}{4}, - \operatorname{atan}{\left(\frac{\sqrt{2} + \sqrt{6}}{- \sqrt{6} + \sqrt{2}} \right)}\right)$$
x in Interval.open(pi/4, -atan((sqrt(2) + sqrt(6))/(-sqrt(6) + sqrt(2))))