Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- x^2+9p^2+2x+6y+2>=0
- 3x+1/5-1-2x/2>x
- 14x+17x-18+35<3,10x+7
- √(x^2-2x)>4-x
- Graphing y =:
- cot(x+(pi/3))
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- cot(x+(pi/ three))<- one
- cotangent of (x plus ( Pi divide by 3)) less than minus 1
- cotangent of (x plus ( Pi divide by three)) less than minus one
- cotx+pi/3<-1
- cot(x+(pi divide by 3))<-1
-
Similar expressions
- cot(x-(pi/3))<-1
- cot(x)+cot(x+pi/2)+2*cot(x+pi/3)>0
- cot(x+(pi/3))<+1
cot(x+(pi/3))<-1 inequation
The solution
You have entered
[src]
/ pi\ cot|x + --| < -1 \ 3 /
$$\cot{\left(x + \frac{\pi}{3} \right)} < -1$$
cot(x + pi/3) < -1
Detail solution
Given the inequality:
$$\cot{\left(x + \frac{\pi}{3} \right)} < -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x + \frac{\pi}{3} \right)} = -1$$
Solve:
$$x_{1} = - \frac{7 \pi}{12}$$
$$x_{1} = - \frac{7 \pi}{12}$$
This roots
$$x_{1} = - \frac{7 \pi}{12}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{7 \pi}{12} - \frac{1}{10}$$
=
$$- \frac{7 \pi}{12} - \frac{1}{10}$$
substitute to the expression
$$\cot{\left(x + \frac{\pi}{3} \right)} < -1$$
$$\cot{\left(\left(- \frac{7 \pi}{12} - \frac{1}{10}\right) + \frac{\pi}{3} \right)} < -1$$
but
Then
$$x < - \frac{7 \pi}{12}$$
no execute
the solution of our inequality is:
$$x > - \frac{7 \pi}{12}$$
$$\cot{\left(x + \frac{\pi}{3} \right)} < -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x + \frac{\pi}{3} \right)} = -1$$
Solve:
$$x_{1} = - \frac{7 \pi}{12}$$
$$x_{1} = - \frac{7 \pi}{12}$$
This roots
$$x_{1} = - \frac{7 \pi}{12}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{7 \pi}{12} - \frac{1}{10}$$
=
$$- \frac{7 \pi}{12} - \frac{1}{10}$$
substitute to the expression
$$\cot{\left(x + \frac{\pi}{3} \right)} < -1$$
$$\cot{\left(\left(- \frac{7 \pi}{12} - \frac{1}{10}\right) + \frac{\pi}{3} \right)} < -1$$
/1 pi\
-cot|-- + --| < -1
\10 4 / but
/1 pi\
-cot|-- + --| > -1
\10 4 / Then
$$x < - \frac{7 \pi}{12}$$
no execute
the solution of our inequality is:
$$x > - \frac{7 \pi}{12}$$
_____
/
-------ο-------
x1
Rapid solution 2
[src]
/ ___ ___\
|\/ 2 + \/ 6 | 2*pi
(-atan|-------------|, ----]
| ___ ___| 3
\\/ 2 - \/ 6 /
$$x\ in\ \left(- \operatorname{atan}{\left(\frac{\sqrt{2} + \sqrt{6}}{- \sqrt{6} + \sqrt{2}} \right)}, \frac{2 \pi}{3}\right]$$
x in Interval.Lopen(-atan((sqrt(2) + sqrt(6))/(-sqrt(6) + sqrt(2))), 2*pi/3)
Rapid solution
[src]
/ / ___ ___\ \ | 2*pi |\/ 2 + \/ 6 | | And|x <= ----, atan|-------------| < x| | 3 | ___ ___| | \ \\/ 6 - \/ 2 / /
$$x \leq \frac{2 \pi}{3} \wedge \operatorname{atan}{\left(\frac{\sqrt{2} + \sqrt{6}}{- \sqrt{2} + \sqrt{6}} \right)} < x$$
(x <= 2*pi/3)∧(atan((sqrt(2) + sqrt(6))/(sqrt(6) - sqrt(2))) < x)