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|+|x+1|>5
- |x+2|*3-x/-x-1<=0
- (1/5)^(x-1)-(1/5)^x<=100
- (4+x)/(4-x)<3
- Graphing y =:
- ctg(3x)
- Derivative of:
-
ctg(3x)
-
1/3
- Sum of series:
-
1/3
- Limit of the function:
- 1/3
-
Identical expressions
- ctg(three x)> one /3
- ctg(3x) greater than 1 divide by 3
- ctg(three x) greater than one divide by 3
- ctg3x>1/3
- ctg(3x)>1 divide by 3
-
Similar expressions
- (6*log2(2x+1))/(3^(1-sqrt(x))-1)<=3^(sqrt(x))*log0,5(2x+1)
ctg(3x)>1/3 inequation
The solution
Detail solution
Given the inequality:
$$\cot{\left(3 x \right)} > \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(3 x \right)} = \frac{1}{3}$$
Solve:
Given the equation
$$\cot{\left(3 x \right)} = \frac{1}{3}$$
transform
$$\cot{\left(3 x \right)} - \frac{1}{3} = 0$$
$$\cot{\left(3 x \right)} - \frac{1}{3} = 0$$
Do replacement
$$w = \cot{\left(3 x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{3}$$
We get the answer: w = 1/3
do backward replacement
$$\cot{\left(3 x \right)} = w$$
substitute w:
$$x_{1} = \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
$$x_{1} = \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
This roots
$$x_{1} = \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
=
$$- \frac{1}{10} + \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
substitute to the expression
$$\cot{\left(3 x \right)} > \frac{1}{3}$$
$$\cot{\left(3 \left(- \frac{1}{10} + \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}\right) \right)} > \frac{1}{3}$$
the solution of our inequality is:
$$x < \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
$$\cot{\left(3 x \right)} > \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(3 x \right)} = \frac{1}{3}$$
Solve:
Given the equation
$$\cot{\left(3 x \right)} = \frac{1}{3}$$
transform
$$\cot{\left(3 x \right)} - \frac{1}{3} = 0$$
$$\cot{\left(3 x \right)} - \frac{1}{3} = 0$$
Do replacement
$$w = \cot{\left(3 x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{3}$$
We get the answer: w = 1/3
do backward replacement
$$\cot{\left(3 x \right)} = w$$
substitute w:
$$x_{1} = \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
$$x_{1} = \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
This roots
$$x_{1} = \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
=
$$- \frac{1}{10} + \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
substitute to the expression
$$\cot{\left(3 x \right)} > \frac{1}{3}$$
$$\cot{\left(3 \left(- \frac{1}{10} + \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}\right) \right)} > \frac{1}{3}$$
-cot(3/10 - acot(1/3)) > 1/3
the solution of our inequality is:
$$x < \frac{\operatorname{acot}{\left(\frac{1}{3} \right)}}{3}$$
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Rapid solution
[src]
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$$0 < x \wedge x < - i \left(\log{\left(\sqrt{\sin^{2}{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)} + \cos^{2}{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)}}{\cos{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)}} \right)}\right)$$
(0 < x)∧(x < -i*(i*atan(sin(-atan(3/4)/6 + pi/6)/cos(-atan(3/4)/6 + pi/6)) + log(sqrt(cos(-atan(3/4)/6 + pi/6)^2 + sin(-atan(3/4)/6 + pi/6)^2))))