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La ecuación:
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Expresar {x} en función de y en la ecuación:
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10*x+3*y=2
-10*x-12*y=-10
Expresiones idénticas
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sin(2z)cos(2z)=1
sin2zcos2z=1
Expresiones con funciones
Seno sin
sin(13π/2−8x)=2/√2
sin(pi-x)+cos(3*pi/2+x)+2*(sin(x))^2=3/2
sin(x)=0,9
sin(((sqrt2mE)l)/h)=sqrt(E)/(U)
sin(x)=-6/8
Coseno cos
cos(2pi×x)-3sin(pi×x)+1=0
cos(x)+x^4-4=0
cos^2(x+(pi/6))=1
cos(3x-pi)=-1
cos𝑥=−1

sin(2z)cos(2*z)=1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

sin(2*z)*cos(2*z) = 1

$$\sin{\left(2 z \right)} \cos{\left(2 z \right)} = 1$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

         /    /         _______________          \\     /    /         _______________          \\
         |    |        /           ___        ___||     |    |        /           ___        ___||
         |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||     |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||
z1 = I*im|atan|- - + ------------------ + -------|| + re|atan|- - + ------------------ + -------||
         \    \  2           2               2   //     \    \  2           2               2   //

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

         /    /                       _____________\\       /    /                       _____________\\
         |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||
         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||
z2 = - re|atan|- + ------- - ----------------------|| - I*im|atan|- + ------- - ----------------------||
         \    \2      2                2           //       \    \2      2                2           //

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

         /    /                       _____________\\       /    /                       _____________\\
         |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||
         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||
z3 = - re|atan|- + ------- + ----------------------|| - I*im|atan|- + ------- + ----------------------||
         \    \2      2                2           //       \    \2      2                2           //

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

         /    /             _____________          \\       /    /             _____________          \\
         |    |      ___   /         ___        ___||       |    |      ___   /         ___        ___||
         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||       |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||
z4 = - re|atan|- + ---------------------- - -------|| - I*im|atan|- + ---------------------- - -------||
         \    \2             2                 2   //       \    \2             2                 2   //

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

z4 = -re(atan(1/2 - sqrt(3)*i/2 + sqrt(2)*sqrt(1 - sqrt(3)*i)/2)) - i*im(atan(1/2 - sqrt(3)*i/2 + sqrt(2)*sqrt(1 - sqrt(3)*i)/2))

Suma y producto de raíces [src]

suma

    /    /         _______________          \\     /    /         _______________          \\       /    /                       _____________\\       /    /                       _____________\\       /    /                       _____________\\       /    /                       _____________\\       /    /             _____________          \\       /    /             _____________          \\
    |    |        /           ___        ___||     |    |        /           ___        ___||       |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||       |    |      ___   /         ___        ___||       |    |      ___   /         ___        ___||
    |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||     |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||       |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||
I*im|atan|- - + ------------------ + -------|| + re|atan|- - + ------------------ + -------|| + - re|atan|- + ------- - ----------------------|| - I*im|atan|- + ------- - ----------------------|| + - re|atan|- + ------- + ----------------------|| - I*im|atan|- + ------- + ----------------------|| + - re|atan|- + ---------------------- - -------|| - I*im|atan|- + ---------------------- - -------||
    \    \  2           2               2   //     \    \  2           2               2   //       \    \2      2                2           //       \    \2      2                2           //       \    \2      2                2           //       \    \2      2                2           //       \    \2             2                 2   //       \    \2             2                 2   //

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

    /    /                       _____________\\     /    /                       _____________\\     /    /             _____________          \\       /    /         _______________          \\       /    /                       _____________\\       /    /                       _____________\\       /    /             _____________          \\     /    /         _______________          \\
    |    |        ___     ___   /         ___ ||     |    |        ___     ___   /         ___ ||     |    |      ___   /         ___        ___||       |    |        /           ___        ___||       |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||       |    |      ___   /         ___        ___||     |    |        /           ___        ___||
    |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||     |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||     |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||       |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||     |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||
- re|atan|- + ------- + ----------------------|| - re|atan|- + ------- - ----------------------|| - re|atan|- + ---------------------- - -------|| + I*im|atan|- - + ------------------ + -------|| - I*im|atan|- + ------- + ----------------------|| - I*im|atan|- + ------- - ----------------------|| - I*im|atan|- + ---------------------- - -------|| + re|atan|- - + ------------------ + -------||
    \    \2      2                2           //     \    \2      2                2           //     \    \2             2                 2   //       \    \  2           2               2   //       \    \2      2                2           //       \    \2      2                2           //       \    \2             2                 2   //     \    \  2           2               2   //

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

producto

/    /    /         _______________          \\     /    /         _______________          \\\ /    /    /                       _____________\\       /    /                       _____________\\\ /    /    /                       _____________\\       /    /                       _____________\\\ /    /    /             _____________          \\       /    /             _____________          \\\
|    |    |        /           ___        ___||     |    |        /           ___        ___||| |    |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||| |    |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||| |    |    |      ___   /         ___        ___||       |    |      ___   /         ___        ___|||
|    |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||     |    |  1   \/  2 - 2*I*\/ 3     I*\/ 3 ||| |    |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||| |    |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||| |    |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||       |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 |||
|I*im|atan|- - + ------------------ + -------|| + re|atan|- - + ------------------ + -------|||*|- re|atan|- + ------- - ----------------------|| - I*im|atan|- + ------- - ----------------------|||*|- re|atan|- + ------- + ----------------------|| - I*im|atan|- + ------- + ----------------------|||*|- re|atan|- + ---------------------- - -------|| - I*im|atan|- + ---------------------- - -------|||
\    \    \  2           2               2   //     \    \  2           2               2   /// \    \    \2      2                2           //       \    \2      2                2           /// \    \    \2      2                2           //       \    \2      2                2           /// \    \    \2             2                 2   //       \    \2             2                 2   ///

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

 /    /    /                       _____________\\     /    /                       _____________\\\ /    /    /                       _____________\\     /    /                       _____________\\\ /    /    /             _____________          \\     /    /             _____________          \\\ /    /    /                         _____________\\     /    /                         _____________\\\
 |    |    |        ___     ___   /         ___ ||     |    |        ___     ___   /         ___ ||| |    |    |        ___     ___   /         ___ ||     |    |        ___     ___   /         ___ ||| |    |    |      ___   /         ___        ___||     |    |      ___   /         ___        ___||| |    |    |          ___     ___   /         ___ ||     |    |          ___     ___   /         ___ |||
 |    |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||     |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||| |    |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||     |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||| |    |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||     |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||| |    |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||     |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  |||
-|I*im|atan|- + ------- + ----------------------|| + re|atan|- + ------- + ----------------------|||*|I*im|atan|- + ------- - ----------------------|| + re|atan|- + ------- - ----------------------|||*|I*im|atan|- + ---------------------- - -------|| + re|atan|- + ---------------------- - -------|||*|I*im|atan|- - + ------- + ----------------------|| + re|atan|- - + ------- + ----------------------|||
 \    \    \2      2                2           //     \    \2      2                2           /// \    \    \2      2                2           //     \    \2      2                2           /// \    \    \2             2                 2   //     \    \2             2                 2   /// \    \    \  2      2                2           //     \    \  2      2                2           ///

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

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

Respuesta numérica [src]

z1 = 0.392699081698724 + 0.329239474231204*i

z2 = 0.392699081698724 - 0.329239474231204*i

z3 = -1.17809724509617 - 0.329239474231204*i

z4 = -1.17809724509617 + 0.329239474231204*i

z4 = -1.17809724509617 + 0.329239474231204*i

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

sin(2*z)*cos(2*z)=1 la ecuación

Solución numérica:

Solución

sin(2z)cos(2*z)=1 la ecuación