Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- (3/(x-6)+(x-6/3))^2<289/16
- sinx*sin(pi/5)-cosx*cos(pi/5)>=((sqrt(2))/2)
- 9^x+11*3^x-93/3^x-82<1
- (((7-cos(4*x)))/2)^(1/4)>2*cos(x)
- Derivative of:
-
tg(3x)
- Integral of d{x}:
- tg(3x)
-
Identical expressions
- tg(3x)< one
- tg(3x) less than 1
- tg(3x) less than one
- tg3x<1
-
Similar expressions
- sqrt3tg(3x+pi/4)<3
- tg^3x+3>tgx+tg^2x
- tg^23x+tg3x>0
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} + \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{1}{10} + \frac{\pi}{12}$$
substitute to the expression
$$\tan{\left(3 x \right)} < 1$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10} + \frac{\pi}{12}\right) \right)} < 1$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{3} + \frac{\pi}{12}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{3} - \frac{1}{10} + \frac{\pi}{12}$$
substitute to the expression
$$\tan{\left(3 x \right)} < 1$$
$$\tan{\left(3 \left(\frac{\pi n}{3} - \frac{1}{10} + \frac{\pi}{12}\right) \right)} < 1$$
/ 3 pi \ tan|- -- + -- + pi*n| < 1 \ 10 4 /
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]
/ / / ___ ___\\ \ | | |\/ 6 - \/ 2 || / pi pi \| Or|And|0 <= x, x < atan|-------------||, And|x <= --, -- < x|| | | | ___ ___|| \ 3 6 /| \ \ \\/ 2 + \/ 6 // /
$$\left(0 \leq x \wedge x < \operatorname{atan}{\left(\frac{- \sqrt{2} + \sqrt{6}}{\sqrt{2} + \sqrt{6}} \right)}\right) \vee \left(x \leq \frac{\pi}{3} \wedge \frac{\pi}{6} < x\right)$$
((x <= pi/3)∧(pi/6 < x))∨((0 <= x)∧(x < atan((sqrt(6) - sqrt(2))/(sqrt(2) + sqrt(6)))))
Rapid solution 2
[src]
/ ___ ___\
|\/ 2 - \/ 6 | pi pi
[0, -atan|-------------|) U (--, --]
| ___ ___| 6 3
\\/ 2 + \/ 6 /
$$x\ in\ \left[0, - \operatorname{atan}{\left(\frac{- \sqrt{6} + \sqrt{2}}{\sqrt{2} + \sqrt{6}} \right)}\right) \cup \left(\frac{\pi}{6}, \frac{\pi}{3}\right]$$
x in Union(Interval.Ropen(0, -atan((-sqrt(6) + sqrt(2))/(sqrt(2) + sqrt(6)))), Interval.Lopen(pi/6, pi/3))