Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
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-
How to use it?
- Inequation:
- tg^2x<9
- (x+6)(x-6)^2(x-32)>0
- sin(x/7)>-1/5
- ctg2x<√3
- Integral of d{x}:
- -1/5
- Limit of the function:
-
-1/5
-
Identical expressions
- sin(x/ seven)>- one / five
- sinus of (x divide by 7) greater than minus 1 divide by 5
- sinus of (x divide by seven) greater than minus one divide by five
- sinx/7>-1/5
- sin(x divide by 7)>-1 divide by 5
-
Similar expressions
- (1/5)^(x-1)-(1/5)^x<=100
- sin(x/7)>+1/5
- ((x-1)^2-1)/5+x/2<(2(x-1)^2+3)/10+(x-1)/2+3
- (2*x-1)/(5-4*x)*(8+x)>=0
- 1/74*sinx/74≤1/148
sin(x/7)>-1/5 inequation
The solution
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/x\ sin|-| > -1/5 \7/
$$\sin{\left(\frac{x}{7} \right)} > - \frac{1}{5}$$
sin(x/7) > -1/5
Detail solution
Given the inequality:
$$\sin{\left(\frac{x}{7} \right)} > - \frac{1}{5}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(\frac{x}{7} \right)} = - \frac{1}{5}$$
Solve:
Given the equation
$$\sin{\left(\frac{x}{7} \right)} = - \frac{1}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{7} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$\frac{x}{7} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$\frac{x}{7} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$\frac{x}{7} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{7}$$
$$x_{1} = 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
$$x_{1} = 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
This roots
$$x_{1} = 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}\right) + - \frac{1}{10}$$
=
$$14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)} - \frac{1}{10}$$
substitute to the expression
$$\sin{\left(\frac{x}{7} \right)} > - \frac{1}{5}$$
$$\sin{\left(\frac{14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)} - \frac{1}{10}}{7} \right)} > - \frac{1}{5}$$
Then
$$x < 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
no execute
one of the solutions of our inequality is:
$$x > 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)} \wedge x < 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
$$\sin{\left(\frac{x}{7} \right)} > - \frac{1}{5}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(\frac{x}{7} \right)} = - \frac{1}{5}$$
Solve:
Given the equation
$$\sin{\left(\frac{x}{7} \right)} = - \frac{1}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{7} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$\frac{x}{7} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$\frac{x}{7} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$\frac{x}{7} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{7}$$
$$x_{1} = 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
$$x_{1} = 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
This roots
$$x_{1} = 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}\right) + - \frac{1}{10}$$
=
$$14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)} - \frac{1}{10}$$
substitute to the expression
$$\sin{\left(\frac{x}{7} \right)} > - \frac{1}{5}$$
$$\sin{\left(\frac{14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)} - \frac{1}{10}}{7} \right)} > - \frac{1}{5}$$
-sin(1/70 - 2*pi*n + asin(1/5)) > -1/5
Then
$$x < 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)}$$
no execute
one of the solutions of our inequality is:
$$x > 14 \pi n - 7 \operatorname{asin}{\left(\frac{1}{5} \right)} \wedge x < 14 \pi n + 7 \operatorname{asin}{\left(\frac{1}{5} \right)} + 7 \pi$$
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x1 x2
Solving inequality on a graph
Rapid solution
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/ / / ___\ \ / / ___\ \\ Or\And\0 <= x, x < - 14*atan\5 + 2*\/ 6 / + 14*pi/, And\x <= 14*pi, - 14*atan\5 - 2*\/ 6 / + 14*pi < x//
$$\left(0 \leq x \wedge x < - 14 \operatorname{atan}{\left(2 \sqrt{6} + 5 \right)} + 14 \pi\right) \vee \left(x \leq 14 \pi \wedge - 14 \operatorname{atan}{\left(5 - 2 \sqrt{6} \right)} + 14 \pi < x\right)$$
((0 <= x)∧(x < -14*atan(5 + 2*sqrt(6)) + 14*pi))∨((x <= 14*pi)∧(-14*atan(5 - 2*sqrt(6)) + 14*pi < x))
Rapid solution 2
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/ ___\ / ___\ [0, - 14*atan\5 + 2*\/ 6 / + 14*pi) U (- 14*atan\5 - 2*\/ 6 / + 14*pi, 14*pi]
$$x\ in\ \left[0, - 14 \operatorname{atan}{\left(2 \sqrt{6} + 5 \right)} + 14 \pi\right) \cup \left(- 14 \operatorname{atan}{\left(5 - 2 \sqrt{6} \right)} + 14 \pi, 14 \pi\right]$$
x in Union(Interval.Ropen(0, -14*atan(2*sqrt(6) + 5) + 14*pi), Interval.Lopen(-14*atan(5 - 2*sqrt(6)) + 14*pi, 14*pi))