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Solving inequalities/ ctg(x)>-1

ctg(x)>-1 inequation

A inequation with variable

The solution

You have entered [src] 
cot(x) > -1
cot⁡(x)>−1\cot{\left(x \right)} > -1 
cot(x) > -1
Detail solution
Given the inequality:
cot⁡(x)>−1\cot{\left(x \right)} > -1
To solve this inequality, we must first solve the corresponding equation:
cot⁡(x)=−1\cot{\left(x \right)} = -1
Solve:
Given the equation
cot⁡(x)=−1\cot{\left(x \right)} = -1
transform
cot⁡(x)+1=0\cot{\left(x \right)} + 1 = 0
cot⁡(x)+1=0\cot{\left(x \right)} + 1 = 0
Do replacement
w=cot⁡(x)w = \cot{\left(x \right)}
Move free summands (without w)
from left part to right part, we given:
w=−1w = -1
We get the answer: w = -1
do backward replacement
cot⁡(x)=w\cot{\left(x \right)} = w
substitute w:
x1=−π4x_{1} = - \frac{\pi}{4}
x1=−π4x_{1} = - \frac{\pi}{4}
This roots
x1=−π4x_{1} = - \frac{\pi}{4}
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1−110x_{0} = x_{1} - \frac{1}{10}
=
−π4−110- \frac{\pi}{4} - \frac{1}{10}
=
−π4−110- \frac{\pi}{4} - \frac{1}{10}
substitute to the expression
cot⁡(x)>−1\cot{\left(x \right)} > -1
cot⁡(−π4−110)>−1\cot{\left(- \frac{\pi}{4} - \frac{1}{10} \right)} > -1
    /1    pi\     
-cot|-- + --| > -1
    \10   4 /

the solution of our inequality is:
x<−π4x < - \frac{\pi}{4}
 _____          
      \    
-------ο-------
       x1
Rapid solution [src] 
   /           3*pi\
And|0 < x, x < ----|
   \            4  /
0<x∧x<3π40 < x \wedge x < \frac{3 \pi}{4} 
(0 < x)∧(x < 3*pi/4)
Rapid solution 2 [src] 
    3*pi 
(0, ----)
     4
x in (0,3π4)x\ in\ \left(0, \frac{3 \pi}{4}\right) 
x in Interval.open(0, 3*pi/4)
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