Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- tg(x)>=-3
- (log2(32x)/log2(x)-5)+(log2(x)-5/log2(32x))>=log2(x^16)+18/log2^2(x)-25
- abs(x+3)<abs(x-5)
- 1-4/|x|<16/x^2
- Derivative of:
-
tg(x)
- Graphing y =:
- tg(x)
- Integral of d{x}:
-
tg(x)
-
Identical expressions
- tg(x)>=- three
- tg(x) greater than or equal to minus 3
- tg(x) greater than or equal to minus three
- tgx>=-3
-
Similar expressions
- 3tg^2x-4sqrt3tgx+3<0
- ctgx>700
- tg((x/7)-(5pi/6))<-sqrt(3)
- tg(x)>=+3
tg(x)>=-3 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} \geq -3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = -3$$
Solve:
Given the equation
$$\tan{\left(x \right)} = -3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-3 \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
$$x_{1} = \pi n - \operatorname{atan}{\left(3 \right)}$$
$$x_{1} = \pi n - \operatorname{atan}{\left(3 \right)}$$
This roots
$$x_{1} = \pi n - \operatorname{atan}{\left(3 \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \operatorname{atan}{\left(3 \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \operatorname{atan}{\left(3 \right)} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq -3$$
$$\tan{\left(\pi n - \operatorname{atan}{\left(3 \right)} - \frac{1}{10} \right)} \geq -3$$
but
Then
$$x \leq \pi n - \operatorname{atan}{\left(3 \right)}$$
no execute
the solution of our inequality is:
$$x \geq \pi n - \operatorname{atan}{\left(3 \right)}$$
$$\tan{\left(x \right)} \geq -3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = -3$$
Solve:
Given the equation
$$\tan{\left(x \right)} = -3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-3 \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
$$x_{1} = \pi n - \operatorname{atan}{\left(3 \right)}$$
$$x_{1} = \pi n - \operatorname{atan}{\left(3 \right)}$$
This roots
$$x_{1} = \pi n - \operatorname{atan}{\left(3 \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \operatorname{atan}{\left(3 \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \operatorname{atan}{\left(3 \right)} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq -3$$
$$\tan{\left(\pi n - \operatorname{atan}{\left(3 \right)} - \frac{1}{10} \right)} \geq -3$$
-tan(1/10 - pi*n + atan(3)) >= -3
but
-tan(1/10 - pi*n + atan(3)) < -3
Then
$$x \leq \pi n - \operatorname{atan}{\left(3 \right)}$$
no execute
the solution of our inequality is:
$$x \geq \pi n - \operatorname{atan}{\left(3 \right)}$$
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Solving inequality on a graph
Rapid solution
[src]
/ / pi\ \ Or|And|0 <= x, x < --|, And(x <= pi, pi - atan(3) <= x)| \ \ 2 / /
$$\left(0 \leq x \wedge x < \frac{\pi}{2}\right) \vee \left(x \leq \pi \wedge \pi - \operatorname{atan}{\left(3 \right)} \leq x\right)$$
((0 <= x)∧(x < pi/2))∨((x <= pi)∧(pi - atan(3) <= x))
Rapid solution 2
[src]
pi
[0, --) U [pi - atan(3), pi]
2
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left[\pi - \operatorname{atan}{\left(3 \right)}, \pi\right]$$
x in Union(Interval.Ropen(0, pi/2), Interval(pi - atan(3), pi))