Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 2*(x-1)-3*(x-2)<x
- (1/2)^(2x+1)<4
- x^2-4*x<=-x+20-x^2
- x-5x+5<0
- Derivative of:
-
tg(3x)
-
-1
- Integral of d{x}:
- tg(3x)
-
-1
- Sum of series:
-
-1
-
Identical expressions
- tg(3x)>- one
- tg(3x) greater than minus 1
- tg(3x) greater than minus one
- tg3x>-1
-
Similar expressions
- tg^3x-2tg^2x>0
- tg(3x)>+1
- tg23x+tg3x>0
- cbrt3tg(3x+п/3)<=1
tg(3x)>-1 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(3 x \right)} > -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = -1$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$3 x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$
This roots
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} - \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{\pi}{12} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(3 x \right)} > -1$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{\pi}{12} - \frac{1}{10}\right) \right)} > -1$$
Then
$$x < \frac{\pi n}{3} - \frac{\pi}{12}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{3} - \frac{\pi}{12}$$
$$\tan{\left(3 x \right)} > -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = -1$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$3 x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$
This roots
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} - \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{\pi}{12} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(3 x \right)} > -1$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{\pi}{12} - \frac{1}{10}\right) \right)} > -1$$
/3 pi \
-tan|-- + -- - pi*n| > -1
\10 4 / Then
$$x < \frac{\pi n}{3} - \frac{\pi}{12}$$
no execute
the solution of our inequality is:
$$x > \frac{\pi n}{3} - \frac{\pi}{12}$$
_____
/
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x1
Solving inequality on a graph
Rapid solution
[src]
/ / pi\ / pi pi \\ Or|And|0 <= x, x < --|, And|x <= --, -- < x|| \ \ 6 / \ 3 4 //
$$\left(0 \leq x \wedge x < \frac{\pi}{6}\right) \vee \left(x \leq \frac{\pi}{3} \wedge \frac{\pi}{4} < x\right)$$
((0 <= x)∧(x < pi/6))∨((x <= pi/3)∧(pi/4 < x))
Rapid solution 2
[src]
pi pi pi
[0, --) U (--, --]
6 4 3
$$x\ in\ \left[0, \frac{\pi}{6}\right) \cup \left(\frac{\pi}{4}, \frac{\pi}{3}\right]$$
x in Union(Interval.Ropen(0, pi/6), Interval.Lopen(pi/4, pi/3))