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sinx>=0 inequation

A inequation with variable

The solution

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sin(x) >= 0
$$\sin{\left(x \right)} \geq 0$$
sin(x) >= 0
Detail solution
Given the inequality:
$$\sin{\left(x \right)} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(x \right)} = 0$$
Solve:
Given the equation
$$\sin{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0

We get:
$$\sin{\left(x \right)} = 0$$
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:
$$x_{0} \leq x_{1}$$
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
$$\sin{\left(x \right)} \geq 0$$
$$\sin{\left(2 \pi n - \frac{1}{10} \right)} \geq 0$$
sin(-1/10 + 2*pi*n) >= 0

but
sin(-1/10 + 2*pi*n) < 0

Then
$$x \leq 2 \pi n$$
no execute
one of the solutions of our inequality is:
$$x \geq 2 \pi n \wedge x \leq 2 \pi n + \pi$$
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        /     \  
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       x1      x2
Solving inequality on a graph
Rapid solution [src]
Or(And(0 <= x, x <= pi), x = 2*pi)
$$\left(0 \leq x \wedge x \leq \pi\right) \vee x = 2 \pi$$
(x = 2*pi))∨((0 <= x)∧(x <= pi)
Rapid solution 2 [src]
[0, pi] U {2*pi}
$$x\ in\ \left[0, \pi\right] \cup \left\{2 \pi\right\}$$
x in Union(FiniteSet(2*pi), Interval(0, pi))