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Other calculators
- Square Inequality Step-by-Step
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How to use it?
- Inequation:
-
3sin^2(2x)+7cos(2x)-3>=0
- ctg(x)>1/sqrt(3)
- ctgx>=-√3
- 4xa^2-(17x+4)a+4x+1>=0
- Canonical form:
- =0
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Identical expressions
- three sin^ two (2x)+7cos(2x)-3>= zero
- 3 sinus of squared (2x) plus 7 co sinus of e of (2x) minus 3 greater than or equal to 0
- three sinus of to the power of two (2x) plus 7 co sinus of e of (2x) minus 3 greater than or equal to zero
- 3sin2(2x)+7cos(2x)-3>=0
- 3sin22x+7cos2x-3>=0
- 3sin²(2x)+7cos(2x)-3>=0
- 3sin to the power of 2(2x)+7cos(2x)-3>=0
- 3sin^22x+7cos2x-3>=0
- 3sin^2(2x)+7cos(2x)-3>=O
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Similar expressions
- 3sin^2(2x)+7cos(2x)+3>=0
- 3sin^2(2x)-7cos(2x)-3>=0
3sin^2(2x)+7cos(2x)-3>=0 inequation
The solution
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[src]
2 3*sin (2*x) + 7*cos(2*x) - 3 >= 0
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 \geq 0$$
3*sin(2*x)^2 + 7*cos(2*x) - 1*3 >= 0
Detail solution
Given the inequality:
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 = 0$$
Solve:
$$x_{1} = - \frac{\pi}{4}$$
$$x_{2} = \frac{\pi}{4}$$
$$x_{3} = - i \operatorname{atanh}{\left(\frac{\sqrt{10}}{5} \right)}$$
$$x_{4} = i \operatorname{atanh}{\left(\frac{\sqrt{10}}{5} \right)}$$
Exclude the complex solutions:
$$x_{1} = - \frac{\pi}{4}$$
$$x_{2} = \frac{\pi}{4}$$
This roots
$$x_{1} = - \frac{\pi}{4}$$
$$x_{2} = \frac{\pi}{4}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{\pi}{4} - \frac{1}{10}$$
=
$$- \frac{\pi}{4} - \frac{1}{10}$$
substitute to the expression
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 \geq 0$$
$$\left(-1\right) 3 + 7 \cos{\left(2 \left(- \frac{\pi}{4} - \frac{1}{10}\right) \right)} + 3 \sin^{2}{\left(2 \left(- \frac{\pi}{4} - \frac{1}{10}\right) \right)} \geq 0$$
but
Then
$$x \leq - \frac{\pi}{4}$$
no execute
one of the solutions of our inequality is:
$$x \geq - \frac{\pi}{4} \wedge x \leq \frac{\pi}{4}$$
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 = 0$$
Solve:
$$x_{1} = - \frac{\pi}{4}$$
$$x_{2} = \frac{\pi}{4}$$
$$x_{3} = - i \operatorname{atanh}{\left(\frac{\sqrt{10}}{5} \right)}$$
$$x_{4} = i \operatorname{atanh}{\left(\frac{\sqrt{10}}{5} \right)}$$
Exclude the complex solutions:
$$x_{1} = - \frac{\pi}{4}$$
$$x_{2} = \frac{\pi}{4}$$
This roots
$$x_{1} = - \frac{\pi}{4}$$
$$x_{2} = \frac{\pi}{4}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{\pi}{4} - \frac{1}{10}$$
=
$$- \frac{\pi}{4} - \frac{1}{10}$$
substitute to the expression
$$3 \sin^{2}{\left(2 x \right)} + 7 \cos{\left(2 x \right)} - 3 \geq 0$$
$$\left(-1\right) 3 + 7 \cos{\left(2 \left(- \frac{\pi}{4} - \frac{1}{10}\right) \right)} + 3 \sin^{2}{\left(2 \left(- \frac{\pi}{4} - \frac{1}{10}\right) \right)} \geq 0$$
2
-3 - 7*sin(1/5) + 3*cos (1/5) >= 0
but
2
-3 - 7*sin(1/5) + 3*cos (1/5) < 0
Then
$$x \leq - \frac{\pi}{4}$$
no execute
one of the solutions of our inequality is:
$$x \geq - \frac{\pi}{4} \wedge x \leq \frac{\pi}{4}$$
_____
/ \
-------•-------•-------
x_1 x_2
Solving inequality on a graph
Rapid solution
[src]
/ / pi\ /3*pi 5*pi\ /7*pi \\ Or|And|0 <= x, x <= --|, And|---- <= x, x <= ----|, And|---- <= x, x < 2*pi|| \ \ 4 / \ 4 4 / \ 4 //
$$\left(0 \leq x \wedge x \leq \frac{\pi}{4}\right) \vee \left(\frac{3 \pi}{4} \leq x \wedge x \leq \frac{5 \pi}{4}\right) \vee \left(\frac{7 \pi}{4} \leq x \wedge x < 2 \pi\right)$$
((0 <= x)∧(x <= pi/4))∨((3*pi/4 <= x)∧(x <= 5*pi/4))∨((7*pi/4 <= x)∧(x < 2*pi))
Rapid solution 2
[src]
pi 3*pi 5*pi 7*pi
[0, --] U [----, ----] U [----, 2*pi)
4 4 4 4
$$x\ in\ \left[0, \frac{\pi}{4}\right] \cup \left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right] \cup \left[\frac{7 \pi}{4}, 2 \pi\right)$$
x in Union(Interval(0, pi/4), Interval(3*pi/4, 5*pi/4), Interval.Ropen(7*pi/4, 2*pi))
The graph