Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- ctgx>=-√3
-
sin(10x)>=1/2
- arccos(x-2)<pi/4
- logx2(x+1)2≤1
- Limit of the function:
-
pi/4
-
Identical expressions
- arccos(x- two)<pi/ four
- arc co sinus of e of (x minus 2) less than Pi divide by 4
- arc co sinus of e of (x minus two) less than Pi divide by four
- arccosx-2<pi/4
- arccos(x-2)<pi divide by 4
-
Similar expressions
- arccos(x+2)<pi/4
arccos(x-2)
The solution
You have entered
[src]
pi
acos(x - 2) < --
4
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
acos(x - 2) < pi/4
Detail solution
Given the inequality:
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{acos}{\left(x - 2 \right)} = \frac{\pi}{4}$$
Solve:
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
This roots
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(\frac{\sqrt{2}}{2} + 2\right)$$
=
$$\frac{\sqrt{2}}{2} + \frac{19}{10}$$
substitute to the expression
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
$$\operatorname{acos}{\left(-2 + \left(\frac{\sqrt{2}}{2} + \frac{19}{10}\right) \right)} < \frac{\pi}{4}$$
/ ___\
| 1 \/ 2 | pi
acos|- -- + -----| < --
\ 10 2 / 4
but
/ ___\
| 1 \/ 2 | pi
acos|- -- + -----| > --
\ 10 2 / 4
Then
$$x < \frac{\sqrt{2}}{2} + 2$$
no execute
the solution of our inequality is:
$$x > \frac{\sqrt{2}}{2} + 2$$
_____
/
-------ο-------
x1
Solving inequality on a graph
Rapid solution
This inequality has no solutions
The solution
You have entered
[src]
pi
acos(x - 2) < --
4
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
acos(x - 2) < pi/4
Detail solution
Given the inequality:
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{acos}{\left(x - 2 \right)} = \frac{\pi}{4}$$
Solve:
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
This roots
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(\frac{\sqrt{2}}{2} + 2\right)$$
=
$$\frac{\sqrt{2}}{2} + \frac{19}{10}$$
substitute to the expression
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
$$\operatorname{acos}{\left(-2 + \left(\frac{\sqrt{2}}{2} + \frac{19}{10}\right) \right)} < \frac{\pi}{4}$$
but
Then
$$x < \frac{\sqrt{2}}{2} + 2$$
no execute
the solution of our inequality is:
$$x > \frac{\sqrt{2}}{2} + 2$$
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{acos}{\left(x - 2 \right)} = \frac{\pi}{4}$$
Solve:
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
This roots
$$x_{1} = \frac{\sqrt{2}}{2} + 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(\frac{\sqrt{2}}{2} + 2\right)$$
=
$$\frac{\sqrt{2}}{2} + \frac{19}{10}$$
substitute to the expression
$$\operatorname{acos}{\left(x - 2 \right)} < \frac{\pi}{4}$$
$$\operatorname{acos}{\left(-2 + \left(\frac{\sqrt{2}}{2} + \frac{19}{10}\right) \right)} < \frac{\pi}{4}$$
/ ___\
| 1 \/ 2 | pi
acos|- -- + -----| < --
\ 10 2 / 4
but
/ ___\
| 1 \/ 2 | pi
acos|- -- + -----| > --
\ 10 2 / 4
Then
$$x < \frac{\sqrt{2}}{2} + 2$$
no execute
the solution of our inequality is:
$$x > \frac{\sqrt{2}}{2} + 2$$
_____
/
-------ο-------
x1
Solving inequality on a graph
Rapid solution
This inequality has no solutions