Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- ctg(x)<=-1
- tgx>=(-1/√3)
- tgx>=0
- log(5,(x-2)(24+2x-x^2))+log(5,(9-x)/(24+2x-x^2))⩽-1+log(5,12x)
- Integral of d{x}:
-
tgx
- Derivative of:
-
tgx
- Graphing y =:
-
tgx
- Canonical form:
- =0
-
Identical expressions
- tgx>= zero
- tgx greater than or equal to 0
- tgx greater than or equal to zero
- tgx>=O
-
Similar expressions
- ctg(x)<=-1
- tg(x/7-5пи/6)<-√3
tgx>=0 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 0$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(x \right)} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$x = \pi n$$
, where n - is a integer
$$x_{1} = \pi n$$
$$x_{1} = \pi n$$
This roots
$$x_{1} = \pi n$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\pi n + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq 0$$
$$\tan{\left(\pi n - \frac{1}{10} \right)} \geq 0$$
but
Then
$$x \leq \pi n$$
no execute
the solution of our inequality is:
$$x \geq \pi n$$
$$\tan{\left(x \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 0$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\tan{\left(x \right)} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$x = \pi n$$
, where n - is a integer
$$x_{1} = \pi n$$
$$x_{1} = \pi n$$
This roots
$$x_{1} = \pi n$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\pi n + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq 0$$
$$\tan{\left(\pi n - \frac{1}{10} \right)} \geq 0$$
tan(-1/10 + pi*n) >= 0
but
tan(-1/10 + pi*n) < 0
Then
$$x \leq \pi n$$
no execute
the solution of our inequality is:
$$x \geq \pi n$$
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x1
Solving inequality on a graph
Rapid solution
[src]
/ / pi\ \ Or|And|0 <= x, x < --|, x = pi| \ \ 2 / /
$$\left(0 \leq x \wedge x < \frac{\pi}{2}\right) \vee x = \pi$$
(x = pi))∨((0 <= x)∧(x < pi/2)
Rapid solution 2
[src]
pi
[0, --) U {pi}
2
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left\{\pi\right\}$$
x in Union(FiniteSet(pi), Interval.Ropen(0, pi/2))