Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- x^2*log(16)*x*1/log(x)>=log(16)*1/log(x^5)+x*log(2)*1/log(x)
- 3x^2+18*x>0
- 2^log(x)*1+x^log(x)<=256
- 0.64-25x^2<0
- Derivative of:
-
tg(3x)
- Integral of d{x}:
- tg(3x)
-
Identical expressions
- tg(three x)<3
- tg(3x) less than 3
- tg(three x) less than 3
- tg3x<3
-
Similar expressions
- tg(3x/4+pi/4)>=-3/3
- tg3x>-2
tg(3x)<3 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(3 x \right)} < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = 3$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = 3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Or
$$3 x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
This roots
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{1}{10} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
substitute to the expression
$$\tan{\left(3 x \right)} < 3$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10} + \frac{\operatorname{atan}{\left(3 \right)}}{3}\right) \right)} < 3$$
the solution of our inequality is:
$$x < \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
$$\tan{\left(3 x \right)} < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(3 x \right)} = 3$$
Solve:
Given the equation
$$\tan{\left(3 x \right)} = 3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Or
$$3 x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
This roots
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{1}{10} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
substitute to the expression
$$\tan{\left(3 x \right)} < 3$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10} + \frac{\operatorname{atan}{\left(3 \right)}}{3}\right) \right)} < 3$$
tan(-3/10 + pi*n + atan(3)) < 3
the solution of our inequality is:
$$x < \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(3 \right)}}{3}$$
_____
\
-------ο-------
x1
Solving inequality on a graph
Rapid solution
[src]
/ / / / / atan(3/4) pi\\ \\ \ | | | |sin|- --------- + --|| / _________________________________________________\|| | | | | | \ 6 6 /| | / 2/ atan(3/4) pi\ 2/ atan(3/4) pi\ ||| / pi pi \| Or|And|0 <= x, x < -I*|I*atan|---------------------| + log| / cos |- --------- + --| + sin |- --------- + --| |||, And|x <= --, -- < x|| | | | | / atan(3/4) pi\| \\/ \ 6 6 / \ 6 6 / /|| \ 3 6 /| | | | |cos|- --------- + --|| || | \ \ \ \ \ 6 6 // // /
$$\left(0 \leq x \wedge x < - i \left(\log{\left(\sqrt{\sin^{2}{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)} + \cos^{2}{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)}}{\cos{\left(- \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{6} + \frac{\pi}{6} \right)}} \right)}\right)\right) \vee \left(x \leq \frac{\pi}{3} \wedge \frac{\pi}{6} < x\right)$$
((x <= pi/3)∧(pi/6 < x))∨((0 <= x)∧(x < -i*(i*atan(sin(-atan(3/4)/6 + pi/6)/cos(-atan(3/4)/6 + pi/6)) + log(sqrt(cos(-atan(3/4)/6 + pi/6)^2 + sin(-atan(3/4)/6 + pi/6)^2)))))