Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 1/3-x/2^2>sqrt(3)
- (4-x)√4+3x-x²≤0
- log(1/2)(1-x)>=-3
- logsqrt3x<=2
- Integral of d{x}:
-
cosx
- Derivative of:
-
cosx
-
sin2x
- Graphing y =:
-
cosx
-
sin2x
- Sum of series:
- sin2x
-
Identical expressions
- cosx>sin2x
- co sinus of e of x greater than sinus of 2x
-
Similar expressions
- 2sin^2x+3sinxcosx-3cos^2x>1
- sin^2(x)<0,25
- sin(x)^4+cos(x)^4<-1
- cos^2x>sin^2x+0,5
- arccos((x+2)/2)<(3*pi/4)
cosx>sin2x inequation
The solution
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[src]
cos(x) > sin(2*x)
$$\cos{\left(x \right)} > \sin{\left(2 x \right)}$$
cos(x) > sin(2*x)
Detail solution
Given the inequality:
$$\cos{\left(x \right)} > \sin{\left(2 x \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(x \right)} = \sin{\left(2 x \right)}$$
Solve:
$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
This roots
$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{\pi}{2} - \frac{1}{10}$$
=
$$- \frac{\pi}{2} - \frac{1}{10}$$
substitute to the expression
$$\cos{\left(x \right)} > \sin{\left(2 x \right)}$$
$$\cos{\left(- \frac{\pi}{2} - \frac{1}{10} \right)} > \sin{\left(2 \left(- \frac{\pi}{2} - \frac{1}{10}\right) \right)}$$
Then
$$x < - \frac{\pi}{2}$$
no execute
one of the solutions of our inequality is:
$$x > - \frac{\pi}{2} \wedge x < \frac{\pi}{6}$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > - \frac{\pi}{2} \wedge x < \frac{\pi}{6}$$
$$x > \frac{\pi}{2} \wedge x < \frac{5 \pi}{6}$$
$$\cos{\left(x \right)} > \sin{\left(2 x \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(x \right)} = \sin{\left(2 x \right)}$$
Solve:
$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
This roots
$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{\pi}{2} - \frac{1}{10}$$
=
$$- \frac{\pi}{2} - \frac{1}{10}$$
substitute to the expression
$$\cos{\left(x \right)} > \sin{\left(2 x \right)}$$
$$\cos{\left(- \frac{\pi}{2} - \frac{1}{10} \right)} > \sin{\left(2 \left(- \frac{\pi}{2} - \frac{1}{10}\right) \right)}$$
-sin(1/10) > sin(1/5)
Then
$$x < - \frac{\pi}{2}$$
no execute
one of the solutions of our inequality is:
$$x > - \frac{\pi}{2} \wedge x < \frac{\pi}{6}$$
_____ _____
/ \ / \
-------ο-------ο-------ο-------ο-------
x_1 x_2 x_3 x_4Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > - \frac{\pi}{2} \wedge x < \frac{\pi}{6}$$
$$x > \frac{\pi}{2} \wedge x < \frac{5 \pi}{6}$$
Solving inequality on a graph
Rapid solution
[src]
/ / pi\ /pi 5*pi\ /3*pi \\ Or|And|0 <= x, x < --|, And|-- < x, x < ----|, And|---- < x, x < 2*pi|| \ \ 6 / \2 6 / \ 2 //
$$\left(0 \leq x \wedge x < \frac{\pi}{6}\right) \vee \left(\frac{\pi}{2} < x \wedge x < \frac{5 \pi}{6}\right) \vee \left(\frac{3 \pi}{2} < x \wedge x < 2 \pi\right)$$
((0 <= x)∧(x < pi/6))∨((pi/2 < x)∧(x < 5*pi/6))∨((3*pi/2 < x)∧(x < 2*pi))
Rapid solution 2
[src]
pi pi 5*pi 3*pi
[0, --) U (--, ----) U (----, 2*pi)
6 2 6 2
$$x\ in\ \left[0, \frac{\pi}{6}\right) \cup \left(\frac{\pi}{2}, \frac{5 \pi}{6}\right) \cup \left(\frac{3 \pi}{2}, 2 \pi\right)$$
x in Union(Interval.Ropen(0, pi/6), Interval.open(pi/2, 5*pi/6), Interval.open(3*pi/2, 2*pi))
The graph