Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- log2(1-x)>log2(2x-8)
- y^2-4*x+8>0
- 4x−3x**2−9≤0
- (x-4)^2>16-x^2
- Derivative of:
-
sin(x)
- -√3/2
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)>-√ three / two
- sinus of (x) greater than minus √3 divide by 2
- sinus of (x) greater than minus √ three divide by two
- sinx>-√3/2
- sin(x)>-√3 divide by 2
-
Similar expressions
- sin<=-(√3)/2
- cos(2x-(pi/4))x≤-(√3/2)
- sinx/3>0
- sin(x)>+√3/2
- sinx<-1/4
- sqrt(2sinx)<1
- sinx>-√3/2
sin(x)>-√3/2 inequation
The solution
You have entered
[src]
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-\/ 3
sin(x) > -------
2
$$\sin{\left(x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
sin(x) > (-sqrt(3))/2
Detail solution
Given the inequality:
$$\sin{\left(x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$x_{2} = 2 \pi n + \frac{4 \pi}{3}$$
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$x_{2} = 2 \pi n + \frac{4 \pi}{3}$$
This roots
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$x_{2} = 2 \pi n + \frac{4 \pi}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(2 \pi n - \frac{\pi}{3}\right) + - \frac{1}{10}$$
=
$$2 \pi n - \frac{\pi}{3} - \frac{1}{10}$$
substitute to the expression
$$\sin{\left(x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
$$\sin{\left(2 \pi n - \frac{\pi}{3} - \frac{1}{10} \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
Then
$$x < 2 \pi n - \frac{\pi}{3}$$
no execute
one of the solutions of our inequality is:
$$x > 2 \pi n - \frac{\pi}{3} \wedge x < 2 \pi n + \frac{4 \pi}{3}$$
$$\sin{\left(x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$x_{2} = 2 \pi n + \frac{4 \pi}{3}$$
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$x_{2} = 2 \pi n + \frac{4 \pi}{3}$$
This roots
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$x_{2} = 2 \pi n + \frac{4 \pi}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(2 \pi n - \frac{\pi}{3}\right) + - \frac{1}{10}$$
=
$$2 \pi n - \frac{\pi}{3} - \frac{1}{10}$$
substitute to the expression
$$\sin{\left(x \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
$$\sin{\left(2 \pi n - \frac{\pi}{3} - \frac{1}{10} \right)} > \frac{\left(-1\right) \sqrt{3}}{2}$$
___
/1 pi \ -\/ 3
-sin|-- + -- - 2*pi*n| > -------
\10 3 / 2
Then
$$x < 2 \pi n - \frac{\pi}{3}$$
no execute
one of the solutions of our inequality is:
$$x > 2 \pi n - \frac{\pi}{3} \wedge x < 2 \pi n + \frac{4 \pi}{3}$$
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/ \
-------ο-------ο-------
x1 x2
Solving inequality on a graph
Rapid solution
[src]
/ / 4*pi\ / 5*pi \\ Or|And|0 <= x, x < ----|, And|x <= 2*pi, ---- < x|| \ \ 3 / \ 3 //
$$\left(0 \leq x \wedge x < \frac{4 \pi}{3}\right) \vee \left(x \leq 2 \pi \wedge \frac{5 \pi}{3} < x\right)$$
((0 <= x)∧(x < 4*pi/3))∨((x <= 2*pi)∧(5*pi/3 < x))
Rapid solution 2
[src]
4*pi 5*pi
[0, ----) U (----, 2*pi]
3 3
$$x\ in\ \left[0, \frac{4 \pi}{3}\right) \cup \left(\frac{5 \pi}{3}, 2 \pi\right]$$
x in Union(Interval.Ropen(0, 4*pi/3), Interval.Lopen(5*pi/3, 2*pi))