Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
2x^2-3x+5>=0
-
tgx>=-1/2
- 6x-x^2>=0
- x(x^2-8x-24)<0
- Integral of d{x}:
-
tgx
- Derivative of:
-
tgx
- Graphing y =:
-
tgx
-
Identical expressions
- tgx>=- one / two
- tgx greater than or equal to minus 1 divide by 2
- tgx greater than or equal to minus one divide by two
- tgx>=-1 divide by 2
-
Similar expressions
- ctg(x/2)=>1+ctg(x)
- ctg(x/3+pi/6)>-sqrt(3)/3
- tgx>=+1/2
tgx>=-1/2 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} \geq - \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = - \frac{1}{2}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
This roots
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}\right) - \frac{1}{10}$$
=
$$\pi n - \operatorname{atan}{\left(\frac{1}{2} \right)} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq - \frac{1}{2}$$
$$\tan{\left(\pi n - \operatorname{atan}{\left(\frac{1}{2} \right)} - \frac{1}{10} \right)} \geq - \frac{1}{2}$$
but
Then
$$x \leq \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
no execute
the solution of our inequality is:
$$x \geq \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
$$\tan{\left(x \right)} \geq - \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = - \frac{1}{2}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
This roots
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}\right) - \frac{1}{10}$$
=
$$\pi n - \operatorname{atan}{\left(\frac{1}{2} \right)} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq - \frac{1}{2}$$
$$\tan{\left(\pi n - \operatorname{atan}{\left(\frac{1}{2} \right)} - \frac{1}{10} \right)} \geq - \frac{1}{2}$$
-tan(1/10 + atan(1/2)) >= -1/2
but
-tan(1/10 + atan(1/2)) < -1/2
Then
$$x \leq \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
no execute
the solution of our inequality is:
$$x \geq \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
_____
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x_1
Solving inequality on a graph
Rapid solution 2
[src]
pi
[0, --) U [pi - atan(1/2), pi)
2
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left[- \operatorname{atan}{\left(\frac{1}{2} \right)} + \pi, \pi\right)$$
x in Union(Interval.Ropen(0, pi/2), Interval.Ropen(pi - atan(1/2), pi))
Rapid solution
[src]
/ / pi\ \ Or|And|0 <= x, x < --|, And(pi - atan(1/2) <= x, x < pi)| \ \ 2 / /
$$\left(0 \leq x \wedge x < \frac{\pi}{2}\right) \vee \left(- \operatorname{atan}{\left(\frac{1}{2} \right)} + \pi \leq x \wedge x < \pi\right)$$
((0 <= x)∧(x < pi/2))∨((x < pi)∧(pi - atan(1/2) <= x))
The graph