Mister Exam

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tg(x)>=2 inequation

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tan(x) >= 2

\tan{\left(x \right)} \geq 2

tan(x) >= 2

Detail solution

Given the inequality:

\tan{\left(x \right)} \geq 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)}

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} \leq 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)} \geq 2

\tan{\left(\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)} \right)} \geq 2

tan(-1/10 + pi*n + atan(2)) >= 2

but

tan(-1/10 + pi*n + atan(2)) < 2

Then

x \leq \pi n + \operatorname{atan}{\left(2 \right)}

no execute
the solution of our inequality is:

x \geq \pi n + \operatorname{atan}{\left(2 \right)}

         _____  
        /
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       x1

Solving inequality on a graph

Rapid solution 2 [src]

          pi 
[atan(2), --)
          2

x\ in\ \left[\operatorname{atan}{\left(2 \right)}, \frac{\pi}{2}\right)

x in Interval.Ropen(atan(2), pi/2)

Rapid solution [src]

   /                  pi\
And|atan(2) <= x, x < --|
   \                  2 /

\operatorname{atan}{\left(2 \right)} \leq x \wedge x < \frac{\pi}{2}

(atan(2) <= x)∧(x < pi/2)