Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
tgx>=-1
- logx(4x-3)>=2
- 4(x+5)-40≥-5+x
- 2x²+6x>=0
- Integral of d{x}:
-
tgx
- Derivative of:
-
tgx
- Graphing y =:
-
tgx
-
Identical expressions
- tgx>=- one
- tgx greater than or equal to minus 1
- tgx greater than or equal to minus one
-
Similar expressions
- tgx>=+1
- tg(x/7-5пи/6)<-√3
tgx>=-1 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} \geq -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = -1$$
Solve:
Given the equation
$$\tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{1} = \pi n - \frac{\pi}{4}$$
This roots
$$x_{1} = \pi n - \frac{\pi}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{4}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{4} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq -1$$
$$\tan{\left(\pi n - \frac{\pi}{4} - \frac{1}{10} \right)} \geq -1$$
but
Then
$$x \leq \pi n - \frac{\pi}{4}$$
no execute
the solution of our inequality is:
$$x \geq \pi n - \frac{\pi}{4}$$
$$\tan{\left(x \right)} \geq -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = -1$$
Solve:
Given the equation
$$\tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{1} = \pi n - \frac{\pi}{4}$$
This roots
$$x_{1} = \pi n - \frac{\pi}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \frac{\pi}{4}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{\pi}{4} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \geq -1$$
$$\tan{\left(\pi n - \frac{\pi}{4} - \frac{1}{10} \right)} \geq -1$$
/1 pi\
-tan|-- + --| >= -1
\10 4 / but
/1 pi\
-tan|-- + --| < -1
\10 4 / Then
$$x \leq \pi n - \frac{\pi}{4}$$
no execute
the solution of our inequality is:
$$x \geq \pi n - \frac{\pi}{4}$$
_____
/
-------•-------
x_1
Solving inequality on a graph
Rapid solution 2
[src]
pi 3*pi
[0, --) U [----, pi)
2 4
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left[\frac{3 \pi}{4}, \pi\right)$$
x in Union(Interval.Ropen(0, pi/2), Interval.Ropen(3*pi/4, pi))
Rapid solution
[src]
/ / pi\ /3*pi \\ Or|And|0 <= x, x < --|, And|---- <= x, x < pi|| \ \ 2 / \ 4 //
$$\left(0 \leq x \wedge x < \frac{\pi}{2}\right) \vee \left(\frac{3 \pi}{4} \leq x \wedge x < \pi\right)$$
((0 <= x)∧(x < pi/2))∨((x < pi)∧(3*pi/4 <= x))
The graph