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sinx/3>0 inequation

A inequation with variable

The solution

You have entered [src]
sin(x)    
------ > 0
  3       
$$\frac{\sin{\left(x \right)}}{3} > 0$$
sin(x)/3 > 0
Detail solution
Given the inequality:
$$\frac{\sin{\left(x \right)}}{3} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(x \right)}}{3} = 0$$
Solve:
Given the equation
$$\frac{\sin{\left(x \right)}}{3} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0

We get:
$$\frac{\sin{\left(x \right)}}{3} = 0$$
Divide both parts of the equation by 1/3

The equation is transformed to
$$\sin{\left(x \right)} = 0$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$x = 2 \pi n$$
$$x = 2 \pi n + \pi$$
, where n - is a integer
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n + \pi$$
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n + \pi$$
This roots
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n + \pi$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$2 \pi n + - \frac{1}{10}$$
=
$$2 \pi n - \frac{1}{10}$$
substitute to the expression
$$\frac{\sin{\left(x \right)}}{3} > 0$$
$$\frac{\sin{\left(2 \pi n - \frac{1}{10} \right)}}{3} > 0$$
sin(-1/10 + 2*pi*n)    
------------------- > 0
         3             

Then
$$x < 2 \pi n$$
no execute
one of the solutions of our inequality is:
$$x > 2 \pi n \wedge x < 2 \pi n + \pi$$
         _____  
        /     \  
-------ο-------ο-------
       x1      x2
Solving inequality on a graph
Rapid solution 2 [src]
(0, pi)
$$x\ in\ \left(0, \pi\right)$$
x in Interval.open(0, pi)
Rapid solution [src]
And(0 < x, x < pi)
$$0 < x \wedge x < \pi$$
(0 < x)∧(x < pi)