Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 14-4*x<2-6*x
- x^2-2*x+12,5>0
- (x-1)sqrt(x^2-x-2)>=0
- (-3)*x^2+32*x+31<=(-2)*x^2+35*x+21
- Derivative of:
-
tanx
- Integral of d{x}:
-
tanx
- Graphing y =:
- tanx
-
Identical expressions
- tanx< three
- tangent of x less than 3
- tangent of x less than three
-
Similar expressions
- tan(x)<=sqrt(3/3)
- tan(x)+cot(x)>=1/(sqrt(3))+sqrt(3)
- tan(x/7-5pi/6)<-√3
tanx<3 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 3$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
$$x_{1} = \pi n + \operatorname{atan}{\left(3 \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(3 \right)}$$
This roots
$$x_{1} = \pi n + \operatorname{atan}{\left(3 \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \operatorname{atan}{\left(3 \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \operatorname{atan}{\left(3 \right)}$$
substitute to the expression
$$\tan{\left(x \right)} < 3$$
$$\tan{\left(\pi n - \frac{1}{10} + \operatorname{atan}{\left(3 \right)} \right)} < 3$$
the solution of our inequality is:
$$x < \pi n + \operatorname{atan}{\left(3 \right)}$$
$$\tan{\left(x \right)} < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 3$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
$$x_{1} = \pi n + \operatorname{atan}{\left(3 \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(3 \right)}$$
This roots
$$x_{1} = \pi n + \operatorname{atan}{\left(3 \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \operatorname{atan}{\left(3 \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \operatorname{atan}{\left(3 \right)}$$
substitute to the expression
$$\tan{\left(x \right)} < 3$$
$$\tan{\left(\pi n - \frac{1}{10} + \operatorname{atan}{\left(3 \right)} \right)} < 3$$
tan(-1/10 + pi*n + atan(3)) < 3
the solution of our inequality is:
$$x < \pi n + \operatorname{atan}{\left(3 \right)}$$
_____
\
-------ο-------
x1
Solving inequality on a graph
Rapid solution
[src]
/ / pi \\ Or|And(0 <= x, x < atan(3)), And|x <= pi, -- < x|| \ \ 2 //
$$\left(0 \leq x \wedge x < \operatorname{atan}{\left(3 \right)}\right) \vee \left(x \leq \pi \wedge \frac{\pi}{2} < x\right)$$
((0 <= x)∧(x < atan(3)))∨((x <= pi)∧(pi/2 < x))
Rapid solution 2
[src]
pi
[0, atan(3)) U (--, pi]
2
$$x\ in\ \left[0, \operatorname{atan}{\left(3 \right)}\right) \cup \left(\frac{\pi}{2}, \pi\right]$$
x in Union(Interval.Ropen(0, atan(3)), Interval.Lopen(pi/2, pi))