Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 2^log(10)*(x^2-4)>=(x+2)^log(10)*2
- sqrt(4*x^2+5*x+1)>x-1
- 6y-9y²-2<0
- x>-4x+3
- Graphing y =:
-
tan(x)
- Derivative of:
-
tan(x)
- Integral of d{x}:
-
tan(x)
-
Identical expressions
- tan(x)<=- one / three
- tangent of (x) less than or equal to minus 1 divide by 3
- tangent of (x) less than or equal to minus one divide by three
- tanx<=-1/3
- tan(x)<=-1 divide by 3
-
Similar expressions
- tan((x+pi)/4)>=0
- tan(x+pi/4)<1
- tan(x)<=+1/3
- tan(x-pi*1/3)>=1/sqrt(3)
tan(x)<=-1/3 inequation
The solution
Detail solution
Given the inequality:
$$\tan{\left(x \right)} \leq - \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = - \frac{1}{3}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = - \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{3} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
, where n - is a integer
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
This roots
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \operatorname{atan}{\left(\frac{1}{3} \right)} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \leq - \frac{1}{3}$$
$$\tan{\left(\pi n - \operatorname{atan}{\left(\frac{1}{3} \right)} - \frac{1}{10} \right)} \leq - \frac{1}{3}$$
the solution of our inequality is:
$$x \leq \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
$$\tan{\left(x \right)} \leq - \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = - \frac{1}{3}$$
Solve:
Given the equation
$$\tan{\left(x \right)} = - \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{3} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
, where n - is a integer
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
This roots
$$x_{1} = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}\right) + - \frac{1}{10}$$
=
$$\pi n - \operatorname{atan}{\left(\frac{1}{3} \right)} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(x \right)} \leq - \frac{1}{3}$$
$$\tan{\left(\pi n - \operatorname{atan}{\left(\frac{1}{3} \right)} - \frac{1}{10} \right)} \leq - \frac{1}{3}$$
-tan(1/10 - pi*n + atan(1/3)) <= -1/3
the solution of our inequality is:
$$x \leq \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
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Solving inequality on a graph
Rapid solution
[src]
/ pi \ And|x <= pi - atan(1/3), -- < x| \ 2 /
$$x \leq \pi - \operatorname{atan}{\left(\frac{1}{3} \right)} \wedge \frac{\pi}{2} < x$$
(pi/2 < x)∧(x <= pi - atan(1/3))
Rapid solution 2
[src]
pi (--, pi - atan(1/3)] 2
$$x\ in\ \left(\frac{\pi}{2}, \pi - \operatorname{atan}{\left(\frac{1}{3} \right)}\right]$$
x in Interval.Lopen(pi/2, pi - atan(1/3))