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Resolver desigualdades/ sin^4(x)+cos^4(x)<=5\8

sin^4(x)+cos^4(x)<=5\8 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
   4         4          
sin (x) + cos (x) <= 5/8
sin⁡4(x)+cos⁡4(x)≤58\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)} \leq \frac{5}{8} 
sin(x)^4 + cos(x)^4 <= 5/8
Solución de la desigualdad en el gráfico
0-80-60-40-202040608002
Respuesta rápida 2 [src] 
 pi  pi     2*pi  5*pi     7*pi  4*pi     5*pi  11*pi 
[--, --] U [----, ----] U [----, ----] U [----, -----]
 6   3       3     6        6     3        3      6
x in [π6,π3]∪[2π3,5π6]∪[7π6,4π3]∪[5π3,11π6]x\ in\ \left[\frac{\pi}{6}, \frac{\pi}{3}\right] \cup \left[\frac{2 \pi}{3}, \frac{5 \pi}{6}\right] \cup \left[\frac{7 \pi}{6}, \frac{4 \pi}{3}\right] \cup \left[\frac{5 \pi}{3}, \frac{11 \pi}{6}\right] 
x in Union(Interval(pi/6, pi/3), Interval(2*pi/3, 5*pi/6), Interval(7*pi/6, 4*pi/3), Interval(5*pi/3, 11*pi/6))
Respuesta rápida [src] 
  /   /pi            pi\     /2*pi            5*pi\     /7*pi            4*pi\     /5*pi            11*pi\\
Or|And|-- <= x, x <= --|, And|---- <= x, x <= ----|, And|---- <= x, x <= ----|, And|---- <= x, x <= -----||
  \   \6             3 /     \ 3               6  /     \ 6               3  /     \ 3                6  //
(π6≤x∧x≤π3)∨(2π3≤x∧x≤5π6)∨(7π6≤x∧x≤4π3)∨(5π3≤x∧x≤11π6)\left(\frac{\pi}{6} \leq x \wedge x \leq \frac{\pi}{3}\right) \vee \left(\frac{2 \pi}{3} \leq x \wedge x \leq \frac{5 \pi}{6}\right) \vee \left(\frac{7 \pi}{6} \leq x \wedge x \leq \frac{4 \pi}{3}\right) \vee \left(\frac{5 \pi}{3} \leq x \wedge x \leq \frac{11 \pi}{6}\right) 
((pi/6 <= x)∧(x <= pi/3))∨((2*pi/3 <= x)∧(x <= 5*pi/6))∨((7*pi/6 <= x)∧(x <= 4*pi/3))∨((5*pi/3 <= x)∧(x <= 11*pi/6))
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