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cos(x)-2sin(2x)>=0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
cos(x) - 2*sin(2*x) >= 0
$$- 2 \sin{\left(2 x \right)} + \cos{\left(x \right)} \geq 0$$
-2*sin(2*x) + cos(x) >= 0
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
  /   /                 /  ____\\     /                       /  ____\\                           \
  |   |                 |\/ 15 ||     |pi                     |\/ 15 ||     /3*pi                \|
Or|And|0 <= x, x <= atan|------||, And|-- <= x, x <= pi - atan|------||, And|---- <= x, x <= 2*pi||
  \   \                 \  15  //     \2                      \  15  //     \ 2                  //
$$\left(0 \leq x \wedge x \leq \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}\right) \vee \left(\frac{\pi}{2} \leq x \wedge x \leq \pi - \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}\right) \vee \left(\frac{3 \pi}{2} \leq x \wedge x \leq 2 \pi\right)$$
((3*pi/2 <= x)∧(x <= 2*pi))∨((0 <= x)∧(x <= atan(sqrt(15)/15)))∨((pi/2 <= x)∧(x <= pi - atan(sqrt(15)/15)))
Respuesta rápida 2 [src]
        /  ____\                  /  ____\                
        |\/ 15 |     pi           |\/ 15 |     3*pi       
[0, atan|------|] U [--, pi - atan|------|] U [----, 2*pi]
        \  15  /     2            \  15  /      2         
$$x\ in\ \left[0, \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}\right] \cup \left[\frac{\pi}{2}, \pi - \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}\right] \cup \left[\frac{3 \pi}{2}, 2 \pi\right]$$
x in Union(Interval(0, atan(sqrt(15)/15)), Interval(pi/2, pi - atan(sqrt(15)/15)), Interval(3*pi/2, 2*pi))