Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 2sqrt(x)<7-|x-10|
- (3-x)²>=6(1-b)
- x^2-2*x-2*1/x^2-2*x+7*x-19*1/x-3-8*x+1*1/x<=0
- (x^2+x+1)^((x-10)/(x-3))<=(x^2+x+1)^3
- Graphing y =:
- sin(x/4)
- Derivative of:
-
sin(x/4)
-
-1/3
- Integral of d{x}:
-
sin(x/4)
- Limit of the function:
-
-1/3
-
Identical expressions
- sin(x/ four)>- one / three
- sinus of (x divide by 4) greater than minus 1 divide by 3
- sinus of (x divide by four) greater than minus one divide by three
- sinx/4>-1/3
- sin(x divide by 4)>-1 divide by 3
-
Similar expressions
- sin(x/4)>+1/3
- (2*n-1)/(3*n+4)<2/3-0.001
- sinx/4<-3\2
- 5x/6+(2x-1)/2-(3x-1)/3≥1
- -90-(1/3)*x>91
- (x-1)/3+(2x+3)/6<(3x-7)/6
- sin(x/4-3)>0
sin(x/4)>-1/3 inequation
The solution
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/x\ sin|-| > -1/3 \4/
$$\sin{\left(\frac{x}{4} \right)} > - \frac{1}{3}$$
sin(x/4) > -1/3
Detail solution
Given the inequality:
$$\sin{\left(\frac{x}{4} \right)} > - \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(\frac{x}{4} \right)} = - \frac{1}{3}$$
Solve:
Given the equation
$$\sin{\left(\frac{x}{4} \right)} = - \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{3} \right)}$$
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{3} \right)} + \pi$$
Or
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{4}$$
$$x_{1} = 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
$$x_{1} = 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
This roots
$$x_{1} = 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}\right) + - \frac{1}{10}$$
=
$$8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)} - \frac{1}{10}$$
substitute to the expression
$$\sin{\left(\frac{x}{4} \right)} > - \frac{1}{3}$$
$$\sin{\left(\frac{8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)} - \frac{1}{10}}{4} \right)} > - \frac{1}{3}$$
Then
$$x < 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
no execute
one of the solutions of our inequality is:
$$x > 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)} \wedge x < 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
$$\sin{\left(\frac{x}{4} \right)} > - \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(\frac{x}{4} \right)} = - \frac{1}{3}$$
Solve:
Given the equation
$$\sin{\left(\frac{x}{4} \right)} = - \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{3} \right)}$$
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{3} \right)} + \pi$$
Or
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{4}$$
$$x_{1} = 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
$$x_{1} = 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
This roots
$$x_{1} = 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}\right) + - \frac{1}{10}$$
=
$$8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)} - \frac{1}{10}$$
substitute to the expression
$$\sin{\left(\frac{x}{4} \right)} > - \frac{1}{3}$$
$$\sin{\left(\frac{8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)} - \frac{1}{10}}{4} \right)} > - \frac{1}{3}$$
-sin(1/40 - 2*pi*n + asin(1/3)) > -1/3
Then
$$x < 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
no execute
one of the solutions of our inequality is:
$$x > 8 \pi n - 4 \operatorname{asin}{\left(\frac{1}{3} \right)} \wedge x < 8 \pi n + 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 4 \pi$$
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x1 x2
Solving inequality on a graph
Rapid solution 2
[src]
/ ___\ / ___\ [0, - 8*atan\3 + 2*\/ 2 / + 8*pi) U (- 8*atan\3 - 2*\/ 2 / + 8*pi, 8*pi]
$$x\ in\ \left[0, - 8 \operatorname{atan}{\left(2 \sqrt{2} + 3 \right)} + 8 \pi\right) \cup \left(- 8 \operatorname{atan}{\left(3 - 2 \sqrt{2} \right)} + 8 \pi, 8 \pi\right]$$
x in Union(Interval.Ropen(0, -8*atan(2*sqrt(2) + 3) + 8*pi), Interval.Lopen(-8*atan(3 - 2*sqrt(2)) + 8*pi, 8*pi))
Rapid solution
[src]
/ / / ___\ \ / / ___\ \\ Or\And\0 <= x, x < - 8*atan\3 + 2*\/ 2 / + 8*pi/, And\x <= 8*pi, - 8*atan\3 - 2*\/ 2 / + 8*pi < x//
$$\left(0 \leq x \wedge x < - 8 \operatorname{atan}{\left(2 \sqrt{2} + 3 \right)} + 8 \pi\right) \vee \left(x \leq 8 \pi \wedge - 8 \operatorname{atan}{\left(3 - 2 \sqrt{2} \right)} + 8 \pi < x\right)$$
((0 <= x)∧(x < -8*atan(3 + 2*sqrt(2)) + 8*pi))∨((x <= 8*pi)∧(-8*atan(3 - 2*sqrt(2)) + 8*pi < x))