Mister Exam
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- Square Inequality Step-by-Step
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- Logarithmic inequality online
-
How to use it?
- Inequation:
- 4x−3x**2−9≤0
- (x-4)^2>16-x^2
- (29/2)x-3>9x+8
- (x+3)*(x-8)<
- Graphing y =:
-
cot(x+pi/6)
-
Identical expressions
- cot(x+pi/ six)>=sqrt(three)/ three
- cotangent of (x plus Pi divide by 6) greater than or equal to square root of (3) divide by 3
- cotangent of (x plus Pi divide by six) greater than or equal to square root of (three) divide by three
- cot(x+pi/6)>=√(3)/3
- cotx+pi/6>=sqrt3/3
- cot(x+pi divide by 6)>=sqrt(3) divide by 3
-
Similar expressions
- cot(x-pi/6)>=sqrt(3)/3
cot(x+pi/6)>=sqrt(3)/3 inequation
The solution
You have entered
[src]
___ / pi\ \/ 3 cot|x + --| >= ----- \ 6 / 3
$$\cot{\left(x + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
cot(x + pi/6) >= sqrt(3)/3
Detail solution
Given the inequality:
$$\cot{\left(x + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x + \frac{\pi}{6} \right)} = \frac{\sqrt{3}}{3}$$
Solve:
$$x_{1} = \frac{\pi}{6}$$
$$x_{1} = \frac{\pi}{6}$$
This roots
$$x_{1} = \frac{\pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\pi}{6}$$
=
$$- \frac{1}{10} + \frac{\pi}{6}$$
substitute to the expression
$$\cot{\left(x + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
$$\cot{\left(\left(- \frac{1}{10} + \frac{\pi}{6}\right) + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
the solution of our inequality is:
$$x \leq \frac{\pi}{6}$$
$$\cot{\left(x + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x + \frac{\pi}{6} \right)} = \frac{\sqrt{3}}{3}$$
Solve:
$$x_{1} = \frac{\pi}{6}$$
$$x_{1} = \frac{\pi}{6}$$
This roots
$$x_{1} = \frac{\pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\pi}{6}$$
=
$$- \frac{1}{10} + \frac{\pi}{6}$$
substitute to the expression
$$\cot{\left(x + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
$$\cot{\left(\left(- \frac{1}{10} + \frac{\pi}{6}\right) + \frac{\pi}{6} \right)} \geq \frac{\sqrt{3}}{3}$$
___
/1 pi\ \/ 3
tan|-- + --| >= -----
\10 6 / 3
the solution of our inequality is:
$$x \leq \frac{\pi}{6}$$
_____
\
-------•-------
x1
Rapid solution 2
[src]
pi 5*pi
[0, --] U (----, pi]
6 6
$$x\ in\ \left[0, \frac{\pi}{6}\right] \cup \left(\frac{5 \pi}{6}, \pi\right]$$
x in Union(Interval(0, pi/6), Interval.Lopen(5*pi/6, pi))
Rapid solution
[src]
/ / pi\ / 5*pi \\ Or|And|0 <= x, x <= --|, And|x <= pi, ---- < x|| \ \ 6 / \ 6 //
$$\left(0 \leq x \wedge x \leq \frac{\pi}{6}\right) \vee \left(x \leq \pi \wedge \frac{5 \pi}{6} < x\right)$$
((0 <= x)∧(x <= pi/6))∨((x <= pi)∧(5*pi/6 < x))