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La ecuación:
Ecuación x^3+3x^2-x-3=0
Ecuación (x+9)^2=36*x
Ecuación x^3-6x^2+11x-6=0
Ecuación a+120=2000/5
Expresar {x} en función de y en la ecuación:
-6*x-12*y=9
9*x-1*y=17
10*x-2*y=11
12*x-3*y=-2
Derivada de:
sin(x)*cos(x)
Gráfico de la función y =:
sin(x)*cos(x)
Forma canónica:
sin(x)*cos(x)
Expresiones idénticas
sin(x)*cos(x)= uno
seno de (x) multiplicar por coseno de (x) es igual a 1
seno de (x) multiplicar por coseno de (x) es igual a uno
sin(x)cos(x)=1
sinxcosx=1
Expresiones semejantes
cos^2x-3sinxcosx+1=0
sinx*cosx+cos^2x=1
2*sin^(2)x-2sqr(3)sinx*cosx-2=0
sinx*cosx=1
Expresiones con funciones
Seno sin
sin(x)=1.5
sin(sin(x))=1
sin(x)=-0.5
sin(-x)=1/2
sin(x)=4/3
Coseno cos
cos(x)+sin(3x)=0
cos(x)=2*x
cos(x)-e^(-x)+x-1=0
cos^2x+cos^22*x-cos^23*x-cos^24*x=0
cos(m/3+x)=1/2

sin(x)*cos(x)=1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

sin(x)*cos(x) = 1

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

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

         /    /                         _____________\\         /    /                         _____________\\
         |    |          ___     ___   /         ___ ||         |    |          ___     ___   /         ___ ||
         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||
x1 = 2*re|atan|- - + ------- + ----------------------|| + 2*I*im|atan|- - + ------- + ----------------------||
         \    \  2      2                2           //         \    \  2      2                2           //

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

           /    /                       _____________\\         /    /                       _____________\\
           |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||
           |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||
x2 = - 2*re|atan|- + ------- - ----------------------|| - 2*I*im|atan|- + ------- - ----------------------||
           \    \2      2                2           //         \    \2      2                2           //

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

           /    /                       _____________\\         /    /                       _____________\\
           |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||
           |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||
x3 = - 2*re|atan|- + ------- + ----------------------|| - 2*I*im|atan|- + ------- + ----------------------||
           \    \2      2                2           //         \    \2      2                2           //

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

           /    /             _____________          \\         /    /             _____________          \\
           |    |      ___   /         ___        ___||         |    |      ___   /         ___        ___||
           |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||
x4 = - 2*re|atan|- + ---------------------- - -------|| - 2*I*im|atan|- + ---------------------- - -------||
           \    \2             2                 2   //         \    \2             2                 2   //

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

x4 = -2*re(atan(1/2 - sqrt(3)*i/2 + sqrt(2)*sqrt(1 - sqrt(3)*i)/2)) - 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   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   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 ||
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|- + ---------------------- - -------||
    \    \  2      2                2           //         \    \  2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2             2                 2   //         \    \2             2                 2   //

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

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

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

producto

/    /    /                         _____________\\         /    /                         _____________\\\ /      /    /                       _____________\\         /    /                       _____________\\\ /      /    /                       _____________\\         /    /                       _____________\\\ /      /    /             _____________          \\         /    /             _____________          \\\
|    |    |          ___     ___   /         ___ ||         |    |          ___     ___   /         ___ ||| |      |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||| |      |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||| |      |    |      ___   /         ___        ___||         |    |      ___   /         ___        ___|||
|    |    |  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   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 |||
|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|- + ---------------------- - -------|||
\    \    \  2      2                2           //         \    \  2      2                2           /// \      \    \2      2                2           //         \    \2      2                2           /// \      \    \2      2                2           //         \    \2      2                2           /// \      \    \2             2                 2   //         \    \2             2                 2   ///

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

    /    /    /                       _____________\\     /    /                       _____________\\\ /    /    /                       _____________\\     /    /                       _____________\\\ /    /    /             _____________          \\     /    /             _____________          \\\ /    /    /                         _____________\\     /    /                         _____________\\\
    |    |    |        ___     ___   /         ___ ||     |    |        ___     ___   /         ___ ||| |    |    |        ___     ___   /         ___ ||     |    |        ___     ___   /         ___ ||| |    |    |      ___   /         ___        ___||     |    |      ___   /         ___        ___||| |    |    |          ___     ___   /         ___ ||     |    |          ___     ___   /         ___ |||
    |    |    |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  |||
-16*|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           ///

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

-16*(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]

x1 = 0.785398163397448 + 0.658478948462408*i

x2 = 0.785398163397448 - 0.658478948462408*i

x3 = -2.35619449019234 - 0.658478948462408*i

x4 = -2.35619449019234 + 0.658478948462408*i

x4 = -2.35619449019234 + 0.658478948462408*i

Gráfico

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sin(x)*cos(x)=1 la ecuación

Solución numérica:

Solución