Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- (49^x-9*7^x+10/7^x-1)+(49^x-11*7^x+33/7^x-6)<=2*7^x-13
- tgx<2
- sin(x)+sqrt(3)cos(x)<1
- log5(3x-1)>0
- Integral of d{x}:
-
tgx
- Derivative of:
-
tgx
- Graphing y =:
-
tgx
-
Identical expressions
- tgx< two
- tgx less than 2
- tgx less than two
-
Similar expressions
- ctg(x/3-П/6)>0
- tg(x/2+П/12)<=-sqrt(3)
tgx<2 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} < 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 2$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 2$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
$$x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}$$
This roots
$$x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \operatorname{atan}{\left(2 \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)}$$
substitute to the expression
$$\tan{\left(x \right)} < 2$$
$$\tan{\left(\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)} \right)} < 2$$
the solution of our inequality is:
$$x < \pi n + \operatorname{atan}{\left(2 \right)}$$
$$\tan{\left(x \right)} < 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 2$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 2$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
$$x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}$$
This roots
$$x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \operatorname{atan}{\left(2 \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)}$$
substitute to the expression
$$\tan{\left(x \right)} < 2$$
$$\tan{\left(\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)} \right)} < 2$$
tan(-1/10 + pi*n + atan(2)) < 2
the solution of our inequality is:
$$x < \pi n + \operatorname{atan}{\left(2 \right)}$$
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x1
Solving inequality on a graph
Rapid solution
[src]
/ / pi \\ Or|And(0 <= x, x < atan(2)), And|x <= pi, -- < x|| \ \ 2 //
$$\left(0 \leq x \wedge x < \operatorname{atan}{\left(2 \right)}\right) \vee \left(x \leq \pi \wedge \frac{\pi}{2} < x\right)$$
((0 <= x)∧(x < atan(2)))∨((x <= pi)∧(pi/2 < x))
Rapid solution 2
[src]
pi
[0, atan(2)) U (--, pi]
2
$$x\ in\ \left[0, \operatorname{atan}{\left(2 \right)}\right) \cup \left(\frac{\pi}{2}, \pi\right]$$
x in Union(Interval.Ropen(0, atan(2)), Interval.Lopen(pi/2, pi))