Sr Examen

sin(2*x)>cos(2*x) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
sin(2*x) > cos(2*x)
$$\sin{\left(2 x \right)} > \cos{\left(2 x \right)}$$
sin(2*x) > cos(2*x)
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
   /             /   ___________\      /   ___________\    \
   |             |  /       ___ |      |  /       ___ |    |
   |             |\/  2 + \/ 2  |      |\/  2 - \/ 2  |    |
And|x < pi - atan|--------------|, atan|--------------| < x|
   |             |   ___________|      |   ___________|    |
   |             |  /       ___ |      |  /       ___ |    |
   \             \\/  2 - \/ 2  /      \\/  2 + \/ 2  /    /
$$x < \pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)} \wedge \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)} < x$$
(atan(sqrt(2 - sqrt(2))/sqrt(2 + sqrt(2))) < x)∧(x < pi - atan(sqrt(2 + sqrt(2))/sqrt(2 - sqrt(2))))
Respuesta rápida 2 [src]
     /   ___________\           /   ___________\ 
     |  /       ___ |           |  /       ___ | 
     |\/  2 - \/ 2  |           |\/  2 + \/ 2  | 
(atan|--------------|, pi - atan|--------------|)
     |   ___________|           |   ___________| 
     |  /       ___ |           |  /       ___ | 
     \\/  2 + \/ 2  /           \\/  2 - \/ 2  / 
$$x\ in\ \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}, \pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)}\right)$$
x in Interval.open(atan(sqrt(2 - sqrt(2))/sqrt(sqrt(2) + 2)), pi - atan(sqrt(sqrt(2) + 2)/sqrt(2 - sqrt(2))))
Gráfico
sin(2*x)>cos(2*x) desigualdades