Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
ctg(x)<-sqrt(3)
- x^2*log(25)(x-3)>=log5(x^2-6x+9)
- tg2x<=tg(pi/3)
- lg^2(x)+3lg(x)-4>0
- Graphing y =:
- tg2x
- Integral of d{x}:
-
tg2x
- Derivative of:
-
tg2x
-
Identical expressions
- tg2x<=tg(pi/ three)
- tg2x less than or equal to tg( Pi divide by 3)
- tg2x less than or equal to tg( Pi divide by three)
- tg2x<=tgpi/3
- tg2x<=tg(pi divide by 3)
-
Similar expressions
- tg^2x-3tgx+2<0
- sin(4x)+cos(4x)*ctg(2x)>1
- ctg^2x>1
- sin(x)(tg(2x))+1>0
tg2x<=tg(pi/3) inequation
The solution
You have entered
[src]
/pi\
tan(2*x) <= tan|--|
\3 /
$$\tan{\left(2 x \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
tan(2*x) <= tan(pi/3)
Detail solution
Given the inequality:
$$\tan{\left(2 x \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(2 x \right)} = \tan{\left(\frac{\pi}{3} \right)}$$
Solve:
Given the equation
$$\tan{\left(2 x \right)} = \tan{\left(\frac{\pi}{3} \right)}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
This roots
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} + \frac{\pi}{6}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{6}$$
substitute to the expression
$$\tan{\left(2 x \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
$$\tan{\left(2 \left(\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{6}\right) \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
the solution of our inequality is:
$$x \leq \frac{\pi n}{2} + \frac{\pi}{6}$$
$$\tan{\left(2 x \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(2 x \right)} = \tan{\left(\frac{\pi}{3} \right)}$$
Solve:
Given the equation
$$\tan{\left(2 x \right)} = \tan{\left(\frac{\pi}{3} \right)}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
This roots
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{2} + \frac{\pi}{6}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{6}$$
substitute to the expression
$$\tan{\left(2 x \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
$$\tan{\left(2 \left(\frac{\pi n}{2} - \frac{1}{10} + \frac{\pi}{6}\right) \right)} \leq \tan{\left(\frac{\pi}{3} \right)}$$
/ 1 pi \ ___ tan|- - + -- + pi*n| <= \/ 3 \ 5 3 /
the solution of our inequality is:
$$x \leq \frac{\pi n}{2} + \frac{\pi}{6}$$
_____
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x1
Solving inequality on a graph
Rapid solution 2
[src]
pi pi pi
[0, --] U (--, --]
6 4 2
$$x\ in\ \left[0, \frac{\pi}{6}\right] \cup \left(\frac{\pi}{4}, \frac{\pi}{2}\right]$$
x in Union(Interval(0, pi/6), Interval.Lopen(pi/4, pi/2))
Rapid solution
[src]
/ / pi\ / pi pi \\ Or|And|0 <= x, x <= --|, And|x <= --, -- < x|| \ \ 6 / \ 2 4 //
$$\left(0 \leq x \wedge x \leq \frac{\pi}{6}\right) \vee \left(x \leq \frac{\pi}{2} \wedge \frac{\pi}{4} < x\right)$$
((0 <= x)∧(x <= pi/6))∨((x <= pi/2)∧(pi/4 < x))