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-2sin(x)cos(x)-10=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

-2*sin(x)*cos(x) - 10 = 0

$$- 2 \sin{\left(x \right)} \cos{\left(x \right)} - 10 = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

           /    /                ________________             \\         /    /                ________________             \\
           |    |         ___   /           ____          ____||         |    |         ___   /           ____          ____||
           |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||         |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||
x1 = - 2*re|atan|- -- + ------------------------- + ----------|| - 2*I*im|atan|- -- + ------------------------- + ----------||
           \    \  10               10                  10    //         \    \  10               10                  10    //

$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}$$

         /    /                           ________________\\         /    /                           ________________\\
         |    |           ____     ___   /           ____ ||         |    |           ____     ___   /           ____ ||
         |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||         |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||
x2 = 2*re|atan|-- - ---------- + -------------------------|| + 2*I*im|atan|-- - ---------- + -------------------------||
         \    \10       10                   10           //         \    \10       10                   10           //

$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)}$$

         /    /              ________________             \\         /    /              ________________             \\
         |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____||
         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||
x3 = 2*re|atan|-- - ------------------------- + ----------|| + 2*I*im|atan|-- - ------------------------- + ----------||
         \    \10               10                  10    //         \    \10               10                  10    //

$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}$$

         /    /              ________________             \\         /    /              ________________             \\
         |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____||
         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||
x4 = 2*re|atan|-- + ------------------------- + ----------|| + 2*I*im|atan|-- + ------------------------- + ----------||
         \    \10               10                  10    //         \    \10               10                  10    //

$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}$$

x4 = 2*re(atan(1/10 + sqrt(2)*sqrt(1 + 3*sqrt(11)*i)/10 + 3*sqrt(11)*i/10)) + 2*i*im(atan(1/10 + sqrt(2)*sqrt(1 + 3*sqrt(11)*i)/10 + 3*sqrt(11)*i/10))

Suma y producto de raíces [src]

suma

      /    /                ________________             \\         /    /                ________________             \\       /    /                           ________________\\         /    /                           ________________\\       /    /              ________________             \\         /    /              ________________             \\       /    /              ________________             \\         /    /              ________________             \\
      |    |         ___   /           ____          ____||         |    |         ___   /           ____          ____||       |    |           ____     ___   /           ____ ||         |    |           ____     ___   /           ____ ||       |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____||       |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____||
      |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||         |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||       |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||         |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||       |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||       |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||
- 2*re|atan|- -- + ------------------------- + ----------|| - 2*I*im|atan|- -- + ------------------------- + ----------|| + 2*re|atan|-- - ---------- + -------------------------|| + 2*I*im|atan|-- - ---------- + -------------------------|| + 2*re|atan|-- - ------------------------- + ----------|| + 2*I*im|atan|-- - ------------------------- + ----------|| + 2*re|atan|-- + ------------------------- + ----------|| + 2*I*im|atan|-- + ------------------------- + ----------||
      \    \  10               10                  10    //         \    \  10               10                  10    //       \    \10       10                   10           //         \    \10       10                   10           //       \    \10               10                  10    //         \    \10               10                  10    //       \    \10               10                  10    //         \    \10               10                  10    //

$$\left(\left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right)$$

      /    /                ________________             \\       /    /                           ________________\\       /    /              ________________             \\       /    /              ________________             \\         /    /                ________________             \\         /    /                           ________________\\         /    /              ________________             \\         /    /              ________________             \\
      |    |         ___   /           ____          ____||       |    |           ____     ___   /           ____ ||       |    |       ___   /           ____          ____||       |    |       ___   /           ____          ____||         |    |         ___   /           ____          ____||         |    |           ____     ___   /           ____ ||         |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____||
      |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||       |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||       |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||       |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||         |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||
- 2*re|atan|- -- + ------------------------- + ----------|| + 2*re|atan|-- - ---------- + -------------------------|| + 2*re|atan|-- - ------------------------- + ----------|| + 2*re|atan|-- + ------------------------- + ----------|| - 2*I*im|atan|- -- + ------------------------- + ----------|| + 2*I*im|atan|-- - ---------- + -------------------------|| + 2*I*im|atan|-- - ------------------------- + ----------|| + 2*I*im|atan|-- + ------------------------- + ----------||
      \    \  10               10                  10    //       \    \10       10                   10           //       \    \10               10                  10    //       \    \10               10                  10    //         \    \  10               10                  10    //         \    \10       10                   10           //         \    \10               10                  10    //         \    \10               10                  10    //

$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}$$

producto

/      /    /                ________________             \\         /    /                ________________             \\\ /    /    /                           ________________\\         /    /                           ________________\\\ /    /    /              ________________             \\         /    /              ________________             \\\ /    /    /              ________________             \\         /    /              ________________             \\\
|      |    |         ___   /           ____          ____||         |    |         ___   /           ____          ____||| |    |    |           ____     ___   /           ____ ||         |    |           ____     ___   /           ____ ||| |    |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____||| |    |    |       ___   /           ____          ____||         |    |       ___   /           ____          ____|||
|      |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||         |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||| |    |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||         |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||| |    |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||| |    |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||         |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 |||
|- 2*re|atan|- -- + ------------------------- + ----------|| - 2*I*im|atan|- -- + ------------------------- + ----------|||*|2*re|atan|-- - ---------- + -------------------------|| + 2*I*im|atan|-- - ---------- + -------------------------|||*|2*re|atan|-- - ------------------------- + ----------|| + 2*I*im|atan|-- - ------------------------- + ----------|||*|2*re|atan|-- + ------------------------- + ----------|| + 2*I*im|atan|-- + ------------------------- + ----------|||
\      \    \  10               10                  10    //         \    \  10               10                  10    /// \    \    \10       10                   10           //         \    \10       10                   10           /// \    \    \10               10                  10    //         \    \10               10                  10    /// \    \    \10               10                  10    //         \    \10               10                  10    ///

$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right)$$

    /    /    /                ________________             \\     /    /                ________________             \\\ /    /    /                           ________________\\     /    /                           ________________\\\ /    /    /              ________________             \\     /    /              ________________             \\\ /    /    /              ________________             \\     /    /              ________________             \\\
    |    |    |         ___   /           ____          ____||     |    |         ___   /           ____          ____||| |    |    |           ____     ___   /           ____ ||     |    |           ____     ___   /           ____ ||| |    |    |       ___   /           ____          ____||     |    |       ___   /           ____          ____||| |    |    |       ___   /           ____          ____||     |    |       ___   /           ____          ____|||
    |    |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||     |    |  1    \/ 2 *\/  1 - 3*I*\/ 11     3*I*\/ 11 ||| |    |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||     |    |1    3*I*\/ 11    \/ 2 *\/  1 - 3*I*\/ 11  ||| |    |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||     |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||| |    |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 ||     |    |1    \/ 2 *\/  1 + 3*I*\/ 11     3*I*\/ 11 |||
-16*|I*im|atan|- -- + ------------------------- + ----------|| + re|atan|- -- + ------------------------- + ----------|||*|I*im|atan|-- - ---------- + -------------------------|| + re|atan|-- - ---------- + -------------------------|||*|I*im|atan|-- - ------------------------- + ----------|| + re|atan|-- - ------------------------- + ----------|||*|I*im|atan|-- + ------------------------- + ----------|| + re|atan|-- + ------------------------- + ----------|||
    \    \    \  10               10                  10    //     \    \  10               10                  10    /// \    \    \10       10                   10           //     \    \10       10                   10           /// \    \    \10               10                  10    //     \    \10               10                  10    /// \    \    \10               10                  10    //     \    \10               10                  10    ///

$$- 16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{3 \sqrt{11} i}{10} + \frac{\sqrt{2} \sqrt{1 - 3 \sqrt{11} i}}{10} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} - \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{10} + \frac{\sqrt{2} \sqrt{1 + 3 \sqrt{11} i}}{10} + \frac{3 \sqrt{11} i}{10} \right)}\right)}\right)$$

-16*(i*im(atan(-1/10 + sqrt(2)*sqrt(1 - 3*i*sqrt(11))/10 + 3*i*sqrt(11)/10)) + re(atan(-1/10 + sqrt(2)*sqrt(1 - 3*i*sqrt(11))/10 + 3*i*sqrt(11)/10)))*(i*im(atan(1/10 - 3*i*sqrt(11)/10 + sqrt(2)*sqrt(1 - 3*i*sqrt(11))/10)) + re(atan(1/10 - 3*i*sqrt(11)/10 + sqrt(2)*sqrt(1 - 3*i*sqrt(11))/10)))*(i*im(atan(1/10 - sqrt(2)*sqrt(1 + 3*i*sqrt(11))/10 + 3*i*sqrt(11)/10)) + re(atan(1/10 - sqrt(2)*sqrt(1 + 3*i*sqrt(11))/10 + 3*i*sqrt(11)/10)))*(i*im(atan(1/10 + sqrt(2)*sqrt(1 + 3*i*sqrt(11))/10 + 3*i*sqrt(11)/10)) + re(atan(1/10 + sqrt(2)*sqrt(1 + 3*i*sqrt(11))/10 + 3*i*sqrt(11)/10)))

Respuesta numérica [src]

x1 = -0.785398163397448 - 1.49661142306319*i

x2 = 2.35619449019234 - 1.49661142306319*i

x3 = -0.785398163397448 + 1.49661142306319*i

x4 = 2.35619449019234 + 1.49661142306319*i

x4 = 2.35619449019234 + 1.49661142306319*i

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-2*sin(x)*cos(x)-10=0 la ecuación

Solución numérica:

Solución

-2sin(x)cos(x)-10=0 la ecuación