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*log(16)*x*1/log(x)>=log(16)*1/log(x^5)+x*log(2)*1/log(x)
- (log(x^2+9)/log(3))*log((4/5))*(3*x)/(x+2)-log((4/5))*(6-x)<=0
- sqrt(4-x)>x+2
- (x^2-x)/(x-1)<=1
- Graphing y =:
- -2*sin(2*x)
- Derivative of:
-
-2*sin(2*x)
-
sqrt(3)
- Integral of d{x}:
-
sqrt(3)
- The double integral of:
- sqrt(3)
-
Identical expressions
- - two *sin(two *x)<sqrt(three)
- minus 2 multiply by sinus of (2 multiply by x) less than square root of (3)
- minus two multiply by sinus of (two multiply by x) less than square root of (three)
- -2*sin(2*x)<√(3)
- -2sin(2x)<sqrt(3)
- -2sin2x<sqrt3
-
Similar expressions
- sqrt(3-2x)<x+2
- 2*sin(2*x)<sqrt(3)
- -2*sin2x>-sqrt(3)
- sqrt3×tg(3/1×x+pi/6)<1
- sqrt3+1<x
- -2sin2x>9
- (-2)*sin(2*x+pi/4)>0
- log(2-x)/log(1/sqrt3)>0
-2*sin(2*x)
The solution
You have entered
[src]
___
-2*sin(2*x) < \/ 3
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
-2*sin(2*x) < sqrt(3)
Detail solution
Given the inequality:
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$- 2 \sin{\left(2 x \right)} = \sqrt{3}$$
Solve:
Given the equation
$$- 2 \sin{\left(2 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -2
The equation is transformed to
$$\sin{\left(2 x \right)} = - \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{3}$$
$$2 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
This roots
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{6}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{6} - \frac{1}{10}$$
substitute to the expression
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
$$- 2 \sin{\left(2 \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} < \sqrt{3}$$
/1 pi \ ___
2*sin|- + -- - 2*pi*n| < \/ 3
\5 3 /
but
/1 pi \ ___
2*sin|- + -- - 2*pi*n| > \/ 3
\5 3 /
Then
$$x < \pi n - \frac{\pi}{6}$$
no execute
one of the solutions of our inequality is:
$$x > \pi n - \frac{\pi}{6} \wedge x < \pi n + \frac{2 \pi}{3}$$
_____
/ \
-------ο-------ο-------
x1 x2
Solving inequality on a graph
Rapid solution
[src]
/ / 2*pi\ / 5*pi \\
Or|And|0 <= x, x < ----|, And|x <= pi, ---- < x||
\ \ 3 / \ 6 //
$$\left(0 \leq x \wedge x < \frac{2 \pi}{3}\right) \vee \left(x \leq \pi \wedge \frac{5 \pi}{6} < x\right)$$
((0 <= x)∧(x < 2*pi/3))∨((x <= pi)∧(5*pi/6 < x))
Rapid solution 2
[src]
2*pi 5*pi
[0, ----) U (----, pi]
3 6
$$x\ in\ \left[0, \frac{2 \pi}{3}\right) \cup \left(\frac{5 \pi}{6}, \pi\right]$$
x in Union(Interval.Ropen(0, 2*pi/3), Interval.Lopen(5*pi/6, pi))
The solution
You have entered
[src]
___ -2*sin(2*x) < \/ 3
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
-2*sin(2*x) < sqrt(3)
Detail solution
Given the inequality:
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$- 2 \sin{\left(2 x \right)} = \sqrt{3}$$
Solve:
Given the equation
$$- 2 \sin{\left(2 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(2 x \right)} = - \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{3}$$
$$2 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
This roots
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{6}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{6} - \frac{1}{10}$$
substitute to the expression
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
$$- 2 \sin{\left(2 \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} < \sqrt{3}$$
but
Then
$$x < \pi n - \frac{\pi}{6}$$
no execute
one of the solutions of our inequality is:
$$x > \pi n - \frac{\pi}{6} \wedge x < \pi n + \frac{2 \pi}{3}$$
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$- 2 \sin{\left(2 x \right)} = \sqrt{3}$$
Solve:
Given the equation
$$- 2 \sin{\left(2 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -2
The equation is transformed to
$$\sin{\left(2 x \right)} = - \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{3}$$
$$2 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
This roots
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{6}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{6} - \frac{1}{10}$$
substitute to the expression
$$- 2 \sin{\left(2 x \right)} < \sqrt{3}$$
$$- 2 \sin{\left(2 \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} < \sqrt{3}$$
/1 pi \ ___
2*sin|- + -- - 2*pi*n| < \/ 3
\5 3 / but
/1 pi \ ___
2*sin|- + -- - 2*pi*n| > \/ 3
\5 3 / Then
$$x < \pi n - \frac{\pi}{6}$$
no execute
one of the solutions of our inequality is:
$$x > \pi n - \frac{\pi}{6} \wedge x < \pi n + \frac{2 \pi}{3}$$
_____
/ \
-------ο-------ο-------
x1 x2
Solving inequality on a graph
Rapid solution
[src]
/ / 2*pi\ / 5*pi \\ Or|And|0 <= x, x < ----|, And|x <= pi, ---- < x|| \ \ 3 / \ 6 //
$$\left(0 \leq x \wedge x < \frac{2 \pi}{3}\right) \vee \left(x \leq \pi \wedge \frac{5 \pi}{6} < x\right)$$
((0 <= x)∧(x < 2*pi/3))∨((x <= pi)∧(5*pi/6 < x))
Rapid solution 2
[src]
2*pi 5*pi
[0, ----) U (----, pi]
3 6
$$x\ in\ \left[0, \frac{2 \pi}{3}\right) \cup \left(\frac{5 \pi}{6}, \pi\right]$$
x in Union(Interval.Ropen(0, 2*pi/3), Interval.Lopen(5*pi/6, pi))