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-8(2x-1)<3x
- x(x-1/2)(8+x)<0
- (x+-3)/x+1(2x+4)_>0
- y>/x+1
- Graphing y =:
-
sin2x
- Derivative of:
-
sin2x
- Sum of series:
- sin2x
-
Identical expressions
- sin two x>-sqrt3/2
- sinus of 2x greater than minus square root of 3 divide by 2
- sinus of two x greater than minus square root of 3 divide by 2
- sin2x>-√3/2
- sin2x>-sqrt3 divide by 2
-
Similar expressions
- cos(2x)>-(sqrt(3)/2)
- sin(3*x)>-sqrt(3)/2
- cos(x)<(-sqrt(3))/2
- 2sin^2x-3sinx+1>0
- arcsin(2x)<=pi*1/3
- sin2x>+sqrt3/2
- sin4x/3>-sqrt(3)/2
sin2x>-sqrt3/2 inequation
The solution
You have entered
[src]
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-\/ 3
sin(2*x) > -------
2
$$\sin{\left(2 x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
sin(2*x) > -sqrt(3)/2
Detail solution
Given the inequality:
$$\sin{\left(2 x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
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
$$\sin{\left(2 x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
$$\sin{\left(2 \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
Then
$$x < \pi n - \frac{\pi}{6}$$
no execute
one of the solutions of our inequality is:
$$x > \pi n - \frac{\pi}{6} \wedge x < \pi n + \frac{2 \pi}{3}$$
$$\sin{\left(2 x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
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
$$\sin{\left(2 x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
$$\sin{\left(2 \left(\pi n - \frac{\pi}{6} - \frac{1}{10}\right) \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
___
/1 pi\ -\/ 3
-sin|- + --| > -------
\5 3 / 2
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-------
x_1 x_2
Solving inequality on a graph
Rapid solution
[src]
/ / 2*pi\ /5*pi \\ Or|And|0 <= x, x < ----|, And|---- < x, x < pi|| \ \ 3 / \ 6 //
$$\left(0 \leq x \wedge x < \frac{2 \pi}{3}\right) \vee \left(\frac{5 \pi}{6} < x \wedge x < \pi\right)$$
((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.open(5*pi/6, pi))
The graph