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+9p^2+2x+6y+2>=0
- 3x+1/5-1-2x/2>x
- x(6x-5)>0
-
49-25x<0
- Derivative of:
-
tg3x
- Graphing y =:
- tg3x
- Integral of d{x}:
-
tg3x
- Canonical form:
- =0
-
Identical expressions
- tg3x>= zero
- tg3x greater than or equal to 0
- tg3x greater than or equal to zero
- tg3x>=O
-
Similar expressions
- tg(3x)<1
- tg^3x+3>tgx+tg^2x
- tg(3*x)>0
tg3x>=0 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(3 x \right)} \geq 0$$
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
$$\tan{\left(3 x \right)} \geq 0$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10}\right) \right)} \geq 0$$
but
Then
$$x \leq \frac{\pi n}{3}$$
no execute
the solution of our inequality is:
$$x \geq \frac{\pi n}{3}$$
$$\tan{\left(3 x \right)} \geq 0$$
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
$$\tan{\left(3 x \right)} \geq 0$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10}\right) \right)} \geq 0$$
tan(-3/10 + pi*n) >= 0
but
tan(-3/10 + pi*n) < 0
Then
$$x \leq \frac{\pi n}{3}$$
no execute
the solution of our inequality is:
$$x \geq \frac{\pi n}{3}$$
_____
/
-------•-------
x1
Solving inequality on a graph
Rapid solution 2
[src]
pi pi
[0, --) U {--}
6 3
$$x\ in\ \left[0, \frac{\pi}{6}\right) \cup \left\{\frac{\pi}{3}\right\}$$
x in Union(FiniteSet(pi/3), Interval.Ropen(0, pi/6))
Rapid solution
[src]
/ / pi\ pi\ Or|And|0 <= x, x < --|, x = --| \ \ 6 / 3 /
$$\left(0 \leq x \wedge x < \frac{\pi}{6}\right) \vee x = \frac{\pi}{3}$$
(x = pi/3))∨((0 <= x)∧(x < pi/6)