sin(2x)

+ desigualdades

¡Resolver la desigualdad!

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)

Respuesta rápida [src]

  /   /                /   ___________\\     /                  /   ___________\    \\
  |   |                |  /       ___ ||     |                  |  /       ___ |    ||
  |   |                |\/  2 - \/ 2  ||     |                  |\/  2 + \/ 2  |    ||
Or|And|0 <= x, x < atan|--------------||, And|x <= pi, pi - atan|--------------| < x||
  |   |                |   ___________||     |                  |   ___________|    ||
  |   |                |  /       ___ ||     |                  |  /       ___ |    ||
  \   \                \\/  2 + \/ 2  //     \                  \\/  2 - \/ 2  /    //

$$\left(0 \leq x \wedge x < \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right) \vee \left(x \leq \pi \wedge \pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)} < x\right)$$

((0 <= x)∧(x < atan(sqrt(2 - sqrt(2))/sqrt(2 + sqrt(2)))))∨((x <= pi)∧(pi - atan(sqrt(2 + sqrt(2))/sqrt(2 - sqrt(2))) < x))

Respuesta rápida 2 [src]

        /   ___________\              /   ___________\     
        |  /       ___ |              |  /       ___ |     
        |\/  2 - \/ 2  |              |\/  2 + \/ 2  |     
[0, atan|--------------|) U (pi - atan|--------------|, pi]
        |   ___________|              |   ___________|     
        |  /       ___ |              |  /       ___ |     
        \\/  2 + \/ 2  /              \\/  2 - \/ 2  /     

$$x\ in\ \left[0, \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right) \cup \left(\pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)}, \pi\right]$$

x in Union(Interval.Ropen(0, atan(sqrt(2 - sqrt(2))/sqrt(sqrt(2) + 2))), Interval.Lopen(pi - atan(sqrt(sqrt(2) + 2)/sqrt(2 - sqrt(2))), pi))

Gráfico