Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
(25^x)+(7*(5^x))+30>=-(5^x)+25
-
tg(x/7-5п/6)<-3
- log0.5(2x-4)<=log0.5(x+1)
- 19x+31>20-3(x-5)
- Integral of d{x}:
-
-3
- Sum of series:
-
-3
- Derivative of:
-
-3
-
Identical expressions
- tg(x/ seven -5п/ six)<- three
- tg(x divide by 7 minus 5п divide by 6) less than minus 3
- tg(x divide by seven minus 5п divide by six) less than minus three
- tgx/7-5п/6<-3
- tg(x divide by 7-5п divide by 6)<-3
-
Similar expressions
- tg(x/7-5п/6)<+3
- tg(x/7+5п/6)<-3
tg(x/7-5п/6)<-3 inequation
The solution
You have entered
[src]
/x 5*pi\ tan|- - ----| < -3 \7 6 /
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} < -3$$
tan(x/7 - 5*pi/6) < -3
Detail solution
Given the inequality:
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} < -3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} = -3$$
Solve:
Given the equation
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} = -3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{7} + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(-3 \right)}$$
Or
$$\frac{x}{7} + \frac{\pi}{6} = \pi n - \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation with the opposite sign, in total:
$$\frac{x}{7} = \pi n - \operatorname{atan}{\left(3 \right)} - \frac{\pi}{6}$$
Divide both parts of the equation by
$$\frac{1}{7}$$
get the intermediate answer:
$$x = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
$$x_{1} = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
$$x_{1} = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
This roots
$$x_{1} = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}\right) - \frac{1}{10}$$
=
$$7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} < -3$$
$$\tan{\left(\frac{7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6} - \frac{1}{10}}{7} - \frac{5 \pi}{6} \right)} < -3$$
the solution of our inequality is:
$$x < 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} < -3$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} = -3$$
Solve:
Given the equation
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} = -3$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{7} + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(-3 \right)}$$
Or
$$\frac{x}{7} + \frac{\pi}{6} = \pi n - \operatorname{atan}{\left(3 \right)}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation with the opposite sign, in total:
$$\frac{x}{7} = \pi n - \operatorname{atan}{\left(3 \right)} - \frac{\pi}{6}$$
Divide both parts of the equation by
$$\frac{1}{7}$$
get the intermediate answer:
$$x = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
$$x_{1} = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
$$x_{1} = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
This roots
$$x_{1} = 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}\right) - \frac{1}{10}$$
=
$$7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6} - \frac{1}{10}$$
substitute to the expression
$$\tan{\left(\frac{x}{7} - \frac{5 \pi}{6} \right)} < -3$$
$$\tan{\left(\frac{7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6} - \frac{1}{10}}{7} - \frac{5 \pi}{6} \right)} < -3$$
-tan(1/70 + atan(3)) < -3
the solution of our inequality is:
$$x < 7 \pi n - 7 \operatorname{atan}{\left(3 \right)} - \frac{7 \pi}{6}$$
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Solving inequality on a graph
Rapid solution
[src]
/ / ____ ____ \\ |7*pi | \/ 10 + 3*\/ 30 || And|---- < x, x < 7*atan|-------------------|| | 3 | ____ ____|| \ \- \/ 30 + 3*\/ 10 //
$$\frac{7 \pi}{3} < x \wedge x < 7 \operatorname{atan}{\left(\frac{\sqrt{10} + 3 \sqrt{30}}{- \sqrt{30} + 3 \sqrt{10}} \right)}$$
(7*pi/3 < x)∧(x < 7*atan((sqrt(10) + 3*sqrt(30))/(-sqrt(30) + 3*sqrt(10))))
Rapid solution 2
[src]
/ ____ ____ \
7*pi | \/ 10 + 3*\/ 30 |
(----, 7*atan|-------------------|)
3 | ____ ____|
\- \/ 30 + 3*\/ 10 /
$$x\ in\ \left(\frac{7 \pi}{3}, 7 \operatorname{atan}{\left(\frac{\sqrt{10} + 3 \sqrt{30}}{- \sqrt{30} + 3 \sqrt{10}} \right)}\right)$$
x in Interval.open(7*pi/3, 7*atan((sqrt(10) + 3*sqrt(30))/(-sqrt(30) + 3*sqrt(10))))
The graph