Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
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How to use it?
- Inequation:
- log(5*x^2+3)/log(x^2-6*x+10)^2<=log(4*x^2+7*x+3)/log(x^2-6*x+10)
- cos(x)≥1/5
- log(2-x)/log(2)*log(2-x)/log(2)+log(absolute(2-x))/log(2)<=2
- cos(8x)>0
- Integral of d{x}:
-
cos(8x)
-
Identical expressions
- cos(8x)> zero
- co sinus of e of (8x) greater than 0
- co sinus of e of (8x) greater than zero
- cos8x>0
-
Similar expressions
- cos(8*x)-1>0
- cos8x>-1
- cos(8*x)>=-sqrt(2)/2
cos(8x)>0 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(8 x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(8 x \right)} = 0$$
Solve:
Given the equation
$$\cos{\left(8 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(8 x \right)} = 0$$
This equation is transformed to
$$8 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$8 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$8 x = \pi n + \frac{\pi}{2}$$
$$8 x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$8$$
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{8} - \frac{\pi}{16}$$
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{8} - \frac{\pi}{16}$$
This roots
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{8} - \frac{\pi}{16}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{8} + \frac{\pi}{16}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{8} - \frac{1}{10} + \frac{\pi}{16}$$
substitute to the expression
$$\cos{\left(8 x \right)} > 0$$
$$\cos{\left(8 \left(\frac{\pi n}{8} - \frac{1}{10} + \frac{\pi}{16}\right) \right)} > 0$$
Then
$$x < \frac{\pi n}{8} + \frac{\pi}{16}$$
no execute
one of the solutions of our inequality is:
$$x > \frac{\pi n}{8} + \frac{\pi}{16} \wedge x < \frac{\pi n}{8} - \frac{\pi}{16}$$
$$\cos{\left(8 x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(8 x \right)} = 0$$
Solve:
Given the equation
$$\cos{\left(8 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(8 x \right)} = 0$$
This equation is transformed to
$$8 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$8 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$8 x = \pi n + \frac{\pi}{2}$$
$$8 x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$8$$
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{8} - \frac{\pi}{16}$$
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{8} - \frac{\pi}{16}$$
This roots
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{8} - \frac{\pi}{16}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{\pi n}{8} + \frac{\pi}{16}\right) + - \frac{1}{10}$$
=
$$\frac{\pi n}{8} - \frac{1}{10} + \frac{\pi}{16}$$
substitute to the expression
$$\cos{\left(8 x \right)} > 0$$
$$\cos{\left(8 \left(\frac{\pi n}{8} - \frac{1}{10} + \frac{\pi}{16}\right) \right)} > 0$$
-sin(-4/5 + pi*n) > 0
Then
$$x < \frac{\pi n}{8} + \frac{\pi}{16}$$
no execute
one of the solutions of our inequality is:
$$x > \frac{\pi n}{8} + \frac{\pi}{16} \wedge x < \frac{\pi n}{8} - \frac{\pi}{16}$$
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x1 x2
Solving inequality on a graph
Rapid solution
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/ / / / ___________ ___________ \ \ \\ | / / / /pi\\ \\ | | | / ___ /pi\ / ___ /pi\| | || | | | |sin|--|| / _____________________\|| | | |\/ 2 + \/ 2 *sin|--| + \/ 2 - \/ 2 *cos|--|| / _____________________\| || | | | | \16/| | / 2/pi\ 2/pi\ ||| | pi | | \16/ \16/| | / 2/pi\ 2/pi\ || || Or|And|0 <= x, x < -I*|I*atan|-------| + log| / cos |--| + sin |--| |||, And|x <= --, -I*|I*atan|-----------------------------------------------| + log| / cos |--| + sin |--| || < x|| | | | | /pi\| \\/ \16/ \16/ /|| | 4 | | ___________ ___________ | \\/ \16/ \16/ /| || | | | |cos|--|| || | | | / ___ /pi\ / ___ /pi\| | || | \ \ \ \16// // | | |\/ 2 + \/ 2 *cos|--| - \/ 2 - \/ 2 *sin|--|| | || \ \ \ \ \16/ \16// / //
$$\left(0 \leq x \wedge x < - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{16} \right)}}{\cos{\left(\frac{\pi}{16} \right)}} \right)}\right)\right) \vee \left(x \leq \frac{\pi}{4} \wedge - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2} \sin{\left(\frac{\pi}{16} \right)} + \sqrt{2 - \sqrt{2}} \cos{\left(\frac{\pi}{16} \right)}}{- \sqrt{2 - \sqrt{2}} \sin{\left(\frac{\pi}{16} \right)} + \sqrt{\sqrt{2} + 2} \cos{\left(\frac{\pi}{16} \right)}} \right)}\right) < x\right)$$
((0 <= x)∧(x < -i*(i*atan(sin(pi/16)/cos(pi/16)) + log(sqrt(cos(pi/16)^2 + sin(pi/16)^2)))))∨((x <= pi/4)∧(-i*(i*atan((sqrt(2 + sqrt(2))*sin(pi/16) + sqrt(2 - sqrt(2))*cos(pi/16))/(sqrt(2 + sqrt(2))*cos(pi/16) - sqrt(2 - sqrt(2))*sin(pi/16))) + log(sqrt(cos(pi/16)^2 + sin(pi/16)^2))) < x))