Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
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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
- Sum of series:
-
√3
- Integral of d{x}:
- √3
-
Identical expressions
- ctg(three x+pi/ three)<√3
- ctg(3x plus Pi divide by 3) less than √3
- ctg(three x plus Pi divide by three) less than √3
- ctg3x+pi/3<√3
- ctg(3x+pi divide by 3)<√3
-
Similar expressions
- ctg(3x-pi/3)<√3
ctg(3x+pi/3)<√3 inequation
The solution
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[src]
/ pi\ ___ cot|3*x + --| < \/ 3 \ 3 /
$$\cot{\left(3 x + \frac{\pi}{3} \right)} < \sqrt{3}$$
cot(3*x + pi/3) < sqrt(3)
Detail solution
Given the inequality:
$$\cot{\left(3 x + \frac{\pi}{3} \right)} < \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(3 x + \frac{\pi}{3} \right)} = \sqrt{3}$$
Solve:
$$x_{1} = - \frac{\pi}{18}$$
$$x_{1} = - \frac{\pi}{18}$$
This roots
$$x_{1} = - \frac{\pi}{18}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{\pi}{18} - \frac{1}{10}$$
=
$$- \frac{\pi}{18} - \frac{1}{10}$$
substitute to the expression
$$\cot{\left(3 x + \frac{\pi}{3} \right)} < \sqrt{3}$$
$$\cot{\left(3 \left(- \frac{\pi}{18} - \frac{1}{10}\right) + \frac{\pi}{3} \right)} < \sqrt{3}$$
but
Then
$$x < - \frac{\pi}{18}$$
no execute
the solution of our inequality is:
$$x > - \frac{\pi}{18}$$
$$\cot{\left(3 x + \frac{\pi}{3} \right)} < \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(3 x + \frac{\pi}{3} \right)} = \sqrt{3}$$
Solve:
$$x_{1} = - \frac{\pi}{18}$$
$$x_{1} = - \frac{\pi}{18}$$
This roots
$$x_{1} = - \frac{\pi}{18}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{\pi}{18} - \frac{1}{10}$$
=
$$- \frac{\pi}{18} - \frac{1}{10}$$
substitute to the expression
$$\cot{\left(3 x + \frac{\pi}{3} \right)} < \sqrt{3}$$
$$\cot{\left(3 \left(- \frac{\pi}{18} - \frac{1}{10}\right) + \frac{\pi}{3} \right)} < \sqrt{3}$$
/3 pi\ ___ tan|-- + --| < \/ 3 \10 3 /
but
/3 pi\ ___ tan|-- + --| > \/ 3 \10 3 /
Then
$$x < - \frac{\pi}{18}$$
no execute
the solution of our inequality is:
$$x > - \frac{\pi}{18}$$
_____
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