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^2-2x)>4-x
- (x+3)^2>(x−23)^2
- 3^(x+2)>81
- (x^2+5*x)/(x-6)>0
- Derivative of:
-
tg3x
- Graphing y =:
- tg3x
- Integral of d{x}:
-
tg3x
- Canonical form:
- =0
-
Identical expressions
- tg3x<= zero
- tg3x less than or equal to 0
- tg3x less than or equal to zero
- tg3x<=O
-
Similar expressions
- tg(3x)>-1
- ctg(3x+pi/3)<√3
- cbrt3tg(3x+п/3)<=1
- ctg(3x)>1/3
tg3x<=0 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(3 x \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = 0$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(3 x \right)} = 0$$
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$3 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3}$$
$$x_{1} = \frac{\pi n}{3}$$
This roots
$$x_{1} = \frac{\pi n}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\frac{\pi n}{3} + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(3 x \right)} \leq 0$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10}\right) \right)} \leq 0$$
the solution of our inequality is:
$$x \leq \frac{\pi n}{3}$$
$$\tan{\left(3 x \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = 0$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\tan{\left(3 x \right)} = 0$$
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$3 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3}$$
$$x_{1} = \frac{\pi n}{3}$$
This roots
$$x_{1} = \frac{\pi n}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\frac{\pi n}{3} + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(3 x \right)} \leq 0$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10}\right) \right)} \leq 0$$
tan(-3/10 + pi*n) <= 0
the solution of our inequality is:
$$x \leq \frac{\pi n}{3}$$
_____
\
-------•-------
x1
Solving inequality on a graph
Rapid solution
[src]
/ / pi pi \ \ Or|And|x <= --, -- < x|, x = 0| \ \ 3 6 / /
$$\left(x \leq \frac{\pi}{3} \wedge \frac{\pi}{6} < x\right) \vee x = 0$$
(x = 0))∨((x <= pi/3)∧(pi/6 < x)
Rapid solution 2
[src]
pi pi
{0} U (--, --]
6 3
$$x\ in\ \left\{0\right\} \cup \left(\frac{\pi}{6}, \frac{\pi}{3}\right]$$
x in Union(FiniteSet(0), Interval.Lopen(pi/6, pi/3))