Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- -8x+7,8_<-12,6x+28,5
- 1,5x+1<|x-1|
- 5-(2-x)/4>=2-x
- x-2x+3/2≤x-1/4
- Graphing y =:
- tg3x
- Derivative of:
-
tg3x
-
-2
- Integral of d{x}:
-
tg3x
-
-2
- Sum of series:
-
-2
-
Identical expressions
- tg3x>- two
- tg3x greater than minus 2
- tg3x greater than minus two
-
Similar expressions
- tg3*(x)>=1/sqrt(3)
- tg3x>+2
- tg(3x)>=-√3
- 5-(2-x)/4>=2-x
- tg(3x/4+pi/4)>=-3/3
- tg(3x)>=sqrt(e)
tg3x>-2 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(3 x \right)} > -2$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = -2$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = -2$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(-2 \right)}$$
Or
$$3 x = \pi n - \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
$$x_{1} = \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
This roots
$$x_{1} = \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(3 x \right)} > -2$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3} - \frac{1}{10}\right) \right)} > -2$$
Then
$$x < \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
$$\tan{\left(3 x \right)} > -2$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = -2$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = -2$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(-2 \right)}$$
Or
$$3 x = \pi n - \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
$$x_{1} = \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
This roots
$$x_{1} = \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(3 x \right)} > -2$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3} - \frac{1}{10}\right) \right)} > -2$$
-tan(3/10 - pi*n + atan(2)) > -2
Then
$$x < \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{3} - \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
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Solving inequality on a graph
Rapid solution
[src]
/ / / / / atan(4/3) pi\ ___ / atan(4/3) pi\\ \ \\ | | | |- sin|- --------- + --| + \/ 3 *cos|- --------- + --|| / _________________________________________________\| || | / pi\ | pi | | \ 6 6 / \ 6 6 /| | / 2/ atan(4/3) pi\ 2/ atan(4/3) pi\ || || Or|And|0 <= x, x < --|, And|x <= --, -I*|I*atan|-----------------------------------------------------| + log| / cos |- --------- + --| + sin |- --------- + --| || < x|| | \ 6 / | 3 | | ___ / atan(4/3) pi\ / atan(4/3) pi\ | \\/ \ 6 6 / \ 6 6 / /| || | | | | \/ 3 *sin|- --------- + --| + cos|- --------- + --| | | || \ \ \ \ \ 6 6 / \ 6 6 / / / //
$$\left(0 \leq x \wedge x < \frac{\pi}{6}\right) \vee \left(x \leq \frac{\pi}{3} \wedge - i \left(\log{\left(\sqrt{\sin^{2}{\left(- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{6} + \frac{\pi}{6} \right)} + \cos^{2}{\left(- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{6} + \frac{\pi}{6} \right)}} \right)} + i \operatorname{atan}{\left(\frac{- \sin{\left(- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{6} + \frac{\pi}{6} \right)} + \sqrt{3} \cos{\left(- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{6} + \frac{\pi}{6} \right)}}{\sqrt{3} \sin{\left(- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{6} + \frac{\pi}{6} \right)} + \cos{\left(- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{6} + \frac{\pi}{6} \right)}} \right)}\right) < x\right)$$
((0 <= x)∧(x < pi/6))∨((x <= pi/3)∧(-i*(i*atan((-sin(-atan(4/3)/6 + pi/6) + sqrt(3)*cos(-atan(4/3)/6 + pi/6))/(sqrt(3)*sin(-atan(4/3)/6 + pi/6) + cos(-atan(4/3)/6 + pi/6))) + log(sqrt(cos(-atan(4/3)/6 + pi/6)^2 + sin(-atan(4/3)/6 + pi/6)^2))) < x))