Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- y>/x+1
- 5^(1-x)>0,2
- logsqrt3x<=2
- (|x|)+(|x-3|)>=3
- Graphing y =:
-
ctg(2x)
- Integral of d{x}:
- ctg(2x)
- Derivative of:
-
ctg(2x)
- Canonical form:
- =0
-
Identical expressions
- ctg(2x)>= zero
- ctg(2x) greater than or equal to 0
- ctg(2x) greater than or equal to zero
- ctg2x>=0
- ctg(2x)>=O
-
Similar expressions
- ctg2x<1
- ctg(2x+pi)≥-sqrt(3)
- arctg^2(x)-4arctgx+3>0
ctg(2x)>=0 inequation
The solution
Detail solution
Given the inequality:
$$\cot{\left(2 x \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(2 x \right)} = 0$$
Solve:
Given the equation
$$\cot{\left(2 x \right)} = 0$$
transform
$$\cot{\left(2 x \right)} - 1 = 0$$
$$\cot{\left(2 x \right)} - 1 = 0$$
Do replacement
$$w = \cot{\left(2 x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\cot{\left(2 x \right)} = w$$
substitute w:
$$x_{1} = \frac{\pi}{4}$$
$$x_{1} = \frac{\pi}{4}$$
This roots
$$x_{1} = \frac{\pi}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\pi}{4}$$
=
$$- \frac{1}{10} + \frac{\pi}{4}$$
substitute to the expression
$$\cot{\left(2 x \right)} \geq 0$$
$$\cot{\left(2 \left(- \frac{1}{10} + \frac{\pi}{4}\right) \right)} \geq 0$$
the solution of our inequality is:
$$x \leq \frac{\pi}{4}$$
$$\cot{\left(2 x \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(2 x \right)} = 0$$
Solve:
Given the equation
$$\cot{\left(2 x \right)} = 0$$
transform
$$\cot{\left(2 x \right)} - 1 = 0$$
$$\cot{\left(2 x \right)} - 1 = 0$$
Do replacement
$$w = \cot{\left(2 x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\cot{\left(2 x \right)} = w$$
substitute w:
$$x_{1} = \frac{\pi}{4}$$
$$x_{1} = \frac{\pi}{4}$$
This roots
$$x_{1} = \frac{\pi}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\pi}{4}$$
=
$$- \frac{1}{10} + \frac{\pi}{4}$$
substitute to the expression
$$\cot{\left(2 x \right)} \geq 0$$
$$\cot{\left(2 \left(- \frac{1}{10} + \frac{\pi}{4}\right) \right)} \geq 0$$
tan(1/5) >= 0
the solution of our inequality is:
$$x \leq \frac{\pi}{4}$$
_____
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x1
Rapid solution
[src]
/ pi \ And|x <= --, 0 < x| \ 4 /
$$x \leq \frac{\pi}{4} \wedge 0 < x$$
(0 < x)∧(x <= pi/4)
Rapid solution 2
[src]
pi
(0, --]
4
$$x\ in\ \left(0, \frac{\pi}{4}\right]$$
x in Interval.Lopen(0, pi/4)