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La ecuación:
Ecuación (3x−36)⋅(x+8)=0
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Ecuación z^4=1
Expresar {x} en función de y en la ecuación:
4*x-1*y=-3
9*x+17*y=13
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6*x+17*y=-11
Expresiones idénticas
dos *sin(x)^(dos)- dos *sin(dos *x)+ cinco *sin((tres *pi/ dos)-x)^(dos)+ dos = cero
2 multiplicar por seno de (x) en el grado (2) menos 2 multiplicar por seno de (2 multiplicar por x) más 5 multiplicar por seno de ((3 multiplicar por número pi dividir por 2) menos x) en el grado (2) más 2 es igual a 0
dos multiplicar por seno de (x) en el grado (dos) menos dos multiplicar por seno de (dos multiplicar por x) más cinco multiplicar por seno de ((tres multiplicar por número pi dividir por dos) menos x) en el grado (dos) más dos es igual a cero
2*sin(x)(2)-2*sin(2*x)+5*sin((3*pi/2)-x)(2)+2=0
2*sinx2-2*sin2*x+5*sin3*pi/2-x2+2=0
2sin(x)^(2)-2sin(2x)+5sin((3pi/2)-x)^(2)+2=0
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2sinx2-2sin2x+5sin3pi/2-x2+2=0
2sinx^2-2sin2x+5sin3pi/2-x^2+2=0
2*sin(x)^(2)-2*sin(2*x)+5*sin((3*pi/2)-x)^(2)+2=O
2*sin(x)^(2)-2*sin(2*x)+5*sin((3*pi dividir por 2)-x)^(2)+2=0
Expresiones semejantes
2*sin(x)^(2)-2*sin(2*x)-5*sin((3*pi/2)-x)^(2)+2=0
2*sin(x)^(2)-2*sin(2*x)+5*sin((3*pi/2)-x)^(2)-2=0
2*sin(x)^(2)+2*sin(2*x)+5*sin((3*pi/2)-x)^(2)+2=0
2*sin(x)^(2)-2*sin(2*x)+5*sin((3*pi/2)+x)^(2)+2=0
2*sinx^(2)-2*sin(2*x)+5*sin((3*pi/2)-x)^(2)+2=0
Expresiones con funciones
Seno sin
sin(2x)=0
sin(3*x)+sin(x)=0
sin(x)=1/2
sin(x)=sin(3)
sin(x)/x=1
Seno sin
sin(2x)=0
sin(3*x)+sin(x)=0
sin(x)=1/2
sin(x)=sin(3)
sin(x)/x=1
Seno sin
sin(2x)=0
sin(3*x)+sin(x)=0
sin(x)=1/2
sin(x)=sin(3)
sin(x)/x=1

2sin(x)^(2)-2sin(2x)+5sin((3*pi/2)-x)^(2)+2=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2                        2/3*pi    \        
2*sin (x) - 2*sin(2*x) + 5*sin |---- - x| + 2 = 0
                               \ 2      /

\left(\left(2 \sin^{2}{\left(x \right)} - 2 \sin{\left(2 x \right)}\right) + 5 \sin^{2}{\left(- x + \frac{3 \pi}{2} \right)}\right) + 2 = 0

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

              /          ___ \                                            
              |44 + 16*\/ 6  |                                            
          atan|--------------|     /             /   ___________________\\
              |           ___|     |             |  /               ___ ||
     pi       \-33 - 12*\/ 6 /     |log(25)   log\\/  5425 + 2200*\/ 6  /|
x1 = -- + -------------------- + I*|------- - ---------------------------|
     2             2               \   2                   2             /

x_{1} = \frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(\sqrt{2200 \sqrt{6} + 5425} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right)

              /          ___ \                                            
              |44 - 16*\/ 6  |                                            
          atan|--------------|     /             /   ___________________\\
              |           ___|     |             |  /               ___ ||
     pi       \-33 + 12*\/ 6 /     |log(25)   log\\/  5425 - 2200*\/ 6  /|
x2 = -- + -------------------- + I*|------- - ---------------------------|
     2             2               \   2                   2             /

x_{2} = \frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(\sqrt{5425 - 2200 \sqrt{6}} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right)

               /   /    /          ___ \\\                                
               |   |    |44 + 16*\/ 6  |||                                
               |   |atan|--------------|||                                
               |   |    |           ___|||                                
               |   |    \-33 - 12*\/ 6 /||        /   ___________________\
               |cos|--------------------||        |4 /               ___ |
               |   \         2          /|        |\/  5425 + 2200*\/ 6  |
x3 = -pi - atan|-------------------------| - I*log|----------------------|
               |   /    /          ___ \\|        \          5           /
               |   |    |44 + 16*\/ 6  |||                                
               |   |atan|--------------|||                                
               |   |    |           ___|||                                
               |   |    \-33 - 12*\/ 6 /||                                
               |sin|--------------------||                                
               \   \         2          //

x_{3} = - \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - i \log{\left(\frac{\sqrt[4]{2200 \sqrt{6} + 5425}}{5} \right)}

               /   /    /          ___ \\\                                
               |   |    |44 - 16*\/ 6  |||                                
               |   |atan|--------------|||                                
               |   |    |           ___|||                                
               |   |    \-33 + 12*\/ 6 /||        /   ___________________\
               |cos|--------------------||        |4 /               ___ |
               |   \         2          /|        |\/  5425 - 2200*\/ 6  |
x4 = -pi - atan|-------------------------| - I*log|----------------------|
               |   /    /          ___ \\|        \          5           /
               |   |    |44 - 16*\/ 6  |||                                
               |   |atan|--------------|||                                
               |   |    |           ___|||                                
               |   |    \-33 + 12*\/ 6 /||                                
               |sin|--------------------||                                
               \   \         2          //

x_{4} = - \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - i \log{\left(\frac{\sqrt[4]{5425 - 2200 \sqrt{6}}}{5} \right)}

x4 = -pi - atan(cos(atan((44 - 16*sqrt(6))/(-33 + 12*sqrt(6)))/2)/sin(atan((44 - 16*sqrt(6))/(-33 + 12*sqrt(6)))/2)) - i*log((5425 - 2200*sqrt(6))^(1/4)/5)

Suma y producto de raíces [src]

suma

                                                                                                                                                          /   /    /          ___ \\\                                             /   /    /          ___ \\\                                
                                                                                                                                                          |   |    |44 + 16*\/ 6  |||                                             |   |    |44 - 16*\/ 6  |||                                
         /          ___ \                                                        /          ___ \                                                         |   |atan|--------------|||                                             |   |atan|--------------|||                                
         |44 + 16*\/ 6  |                                                        |44 - 16*\/ 6  |                                                         |   |    |           ___|||                                             |   |    |           ___|||                                
     atan|--------------|     /             /   ___________________\\        atan|--------------|     /             /   ___________________\\             |   |    \-33 - 12*\/ 6 /||        /   ___________________\             |   |    \-33 + 12*\/ 6 /||        /   ___________________\
         |           ___|     |             |  /               ___ ||            |           ___|     |             |  /               ___ ||             |cos|--------------------||        |4 /               ___ |             |cos|--------------------||        |4 /               ___ |
pi       \-33 - 12*\/ 6 /     |log(25)   log\\/  5425 + 2200*\/ 6  /|   pi       \-33 + 12*\/ 6 /     |log(25)   log\\/  5425 - 2200*\/ 6  /|             |   \         2          /|        |\/  5425 + 2200*\/ 6  |             |   \         2          /|        |\/  5425 - 2200*\/ 6  |
-- + -------------------- + I*|------- - ---------------------------| + -- + -------------------- + I*|------- - ---------------------------| + -pi - atan|-------------------------| - I*log|----------------------| + -pi - atan|-------------------------| - I*log|----------------------|
2             2               \   2                   2             /   2             2               \   2                   2             /             |   /    /          ___ \\|        \          5           /             |   /    /          ___ \\|        \          5           /
                                                                                                                                                          |   |    |44 + 16*\/ 6  |||                                             |   |    |44 - 16*\/ 6  |||                                
                                                                                                                                                          |   |atan|--------------|||                                             |   |atan|--------------|||                                
                                                                                                                                                          |   |    |           ___|||                                             |   |    |           ___|||                                
                                                                                                                                                          |   |    \-33 - 12*\/ 6 /||                                             |   |    \-33 + 12*\/ 6 /||                                
                                                                                                                                                          |sin|--------------------||                                             |sin|--------------------||                                
                                                                                                                                                          \   \         2          //                                             \   \         2          //

\left(\left(- \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - i \log{\left(\frac{\sqrt[4]{2200 \sqrt{6} + 5425}}{5} \right)}\right) + \left(\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(\sqrt{2200 \sqrt{6} + 5425} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right)\right) + \left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(\sqrt{5425 - 2200 \sqrt{6}} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right)\right)\right)\right) + \left(- \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - i \log{\left(\frac{\sqrt[4]{5425 - 2200 \sqrt{6}}}{5} \right)}\right)

                                                       /   /    /          ___ \\\       /   /    /          ___ \\\                                                                                                                                                        
                                                       |   |    |44 + 16*\/ 6  |||       |   |    |44 - 16*\/ 6  |||                                                                                                                                                        
    /          ___ \       /          ___ \            |   |atan|--------------|||       |   |atan|--------------|||                                                                                                                                                        
    |44 + 16*\/ 6  |       |44 - 16*\/ 6  |            |   |    |           ___|||       |   |    |           ___|||                                                                                                                                                        
atan|--------------|   atan|--------------|            |   |    \-33 - 12*\/ 6 /||       |   |    \-33 + 12*\/ 6 /||     /             /   ___________________\\     /             /   ___________________\\        /   ___________________\        /   ___________________\
    |           ___|       |           ___|            |cos|--------------------||       |cos|--------------------||     |             |  /               ___ ||     |             |  /               ___ ||        |4 /               ___ |        |4 /               ___ |
    \-33 - 12*\/ 6 /       \-33 + 12*\/ 6 /            |   \         2          /|       |   \         2          /|     |log(25)   log\\/  5425 - 2200*\/ 6  /|     |log(25)   log\\/  5425 + 2200*\/ 6  /|        |\/  5425 - 2200*\/ 6  |        |\/  5425 + 2200*\/ 6  |
-------------------- + -------------------- - pi - atan|-------------------------| - atan|-------------------------| + I*|------- - ---------------------------| + I*|------- - ---------------------------| - I*log|----------------------| - I*log|----------------------|
         2                      2                      |   /    /          ___ \\|       |   /    /          ___ \\|     \   2                   2             /     \   2                   2             /        \          5           /        \          5           /
                                                       |   |    |44 + 16*\/ 6  |||       |   |    |44 - 16*\/ 6  |||                                                                                                                                                        
                                                       |   |atan|--------------|||       |   |atan|--------------|||                                                                                                                                                        
                                                       |   |    |           ___|||       |   |    |           ___|||                                                                                                                                                        
                                                       |   |    \-33 - 12*\/ 6 /||       |   |    \-33 + 12*\/ 6 /||                                                                                                                                                        
                                                       |sin|--------------------||       |sin|--------------------||                                                                                                                                                        
                                                       \   \         2          //       \   \         2          //

- \pi + \frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}} \right)} + i \left(- \frac{\log{\left(\sqrt{2200 \sqrt{6} + 5425} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right) - i \log{\left(\frac{\sqrt[4]{2200 \sqrt{6} + 5425}}{5} \right)} + i \left(- \frac{\log{\left(\sqrt{5425 - 2200 \sqrt{6}} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right) - i \log{\left(\frac{\sqrt[4]{5425 - 2200 \sqrt{6}}}{5} \right)}

producto

                                                                                                                                                /          /   /    /          ___ \\\                                \ /          /   /    /          ___ \\\                                \
                                                                                                                                                |          |   |    |44 + 16*\/ 6  |||                                | |          |   |    |44 - 16*\/ 6  |||                                |
/         /          ___ \                                            \ /         /          ___ \                                            \ |          |   |atan|--------------|||                                | |          |   |atan|--------------|||                                |
|         |44 + 16*\/ 6  |                                            | |         |44 - 16*\/ 6  |                                            | |          |   |    |           ___|||                                | |          |   |    |           ___|||                                |
|     atan|--------------|     /             /   ___________________\\| |     atan|--------------|     /             /   ___________________\\| |          |   |    \-33 - 12*\/ 6 /||        /   ___________________\| |          |   |    \-33 + 12*\/ 6 /||        /   ___________________\|
|         |           ___|     |             |  /               ___ ||| |         |           ___|     |             |  /               ___ ||| |          |cos|--------------------||        |4 /               ___ || |          |cos|--------------------||        |4 /               ___ ||
|pi       \-33 - 12*\/ 6 /     |log(25)   log\\/  5425 + 2200*\/ 6  /|| |pi       \-33 + 12*\/ 6 /     |log(25)   log\\/  5425 - 2200*\/ 6  /|| |          |   \         2          /|        |\/  5425 + 2200*\/ 6  || |          |   \         2          /|        |\/  5425 - 2200*\/ 6  ||
|-- + -------------------- + I*|------- - ---------------------------||*|-- + -------------------- + I*|------- - ---------------------------||*|-pi - atan|-------------------------| - I*log|----------------------||*|-pi - atan|-------------------------| - I*log|----------------------||
\2             2               \   2                   2             // \2             2               \   2                   2             // |          |   /    /          ___ \\|        \          5           /| |          |   /    /          ___ \\|        \          5           /|
                                                                                                                                                |          |   |    |44 + 16*\/ 6  |||                                | |          |   |    |44 - 16*\/ 6  |||                                |
                                                                                                                                                |          |   |atan|--------------|||                                | |          |   |atan|--------------|||                                |
                                                                                                                                                |          |   |    |           ___|||                                | |          |   |    |           ___|||                                |
                                                                                                                                                |          |   |    \-33 - 12*\/ 6 /||                                | |          |   |    \-33 + 12*\/ 6 /||                                |
                                                                                                                                                |          |sin|--------------------||                                | |          |sin|--------------------||                                |
                                                                                                                                                \          \   \         2          //                                / \          \   \         2          //                                /

\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(\sqrt{2200 \sqrt{6} + 5425} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right)\right) \left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(\sqrt{5425 - 2200 \sqrt{6}} \right)}}{2} + \frac{\log{\left(25 \right)}}{2}\right)\right) \left(- \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{16 \sqrt{6} + 44}{-33 - 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - i \log{\left(\frac{\sqrt[4]{2200 \sqrt{6} + 5425}}{5} \right)}\right) \left(- \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{44 - 16 \sqrt{6}}{-33 + 12 \sqrt{6}} \right)}}{2} \right)}} \right)} - i \log{\left(\frac{\sqrt[4]{5425 - 2200 \sqrt{6}}}{5} \right)}\right)

/                   /     /           ___\         \\ /                   /     /           ___\         \\ /                   /              /           ___\\\ /                   /              /           ___\\\
|                   |  log\217 - 88*\/ 6 /         || |                   |  log\217 + 88*\/ 6 /         || |pi   atan(4/3)     |  log(5)   log\217 - 88*\/ 6 /|| |pi   atan(4/3)     |  log(5)   log\217 + 88*\/ 6 /||
|pi - atan(4/3) + I*|- ------------------- + log(5)||*|pi - atan(4/3) + I*|- ------------------- + log(5)||*|-- + --------- + I*|- ------ + -------------------||*|-- + --------- + I*|- ------ + -------------------||
\                   \           2                  // \                   \           2                  // \2        2         \    2               4         // \2        2         \    2               4         //
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                           4

\frac{\left(- \operatorname{atan}{\left(\frac{4}{3} \right)} + \pi + i \left(- \frac{\log{\left(217 - 88 \sqrt{6} \right)}}{2} + \log{\left(5 \right)}\right)\right) \left(- \operatorname{atan}{\left(\frac{4}{3} \right)} + \pi + i \left(- \frac{\log{\left(88 \sqrt{6} + 217 \right)}}{2} + \log{\left(5 \right)}\right)\right) \left(\frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(5 \right)}}{2} + \frac{\log{\left(217 - 88 \sqrt{6} \right)}}{4}\right)\right) \left(\frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{2} + \frac{\pi}{2} + i \left(- \frac{\log{\left(5 \right)}}{2} + \frac{\log{\left(88 \sqrt{6} + 217 \right)}}{4}\right)\right)}{4}

(pi - atan(4/3) + i*(-log(217 - 88*sqrt(6))/2 + log(5)))*(pi - atan(4/3) + i*(-log(217 + 88*sqrt(6))/2 + log(5)))*(pi/2 + atan(4/3)/2 + i*(-log(5)/2 + log(217 - 88*sqrt(6))/4))*(pi/2 + atan(4/3)/2 + i*(-log(5)/2 + log(217 + 88*sqrt(6))/4))/4

Respuesta numérica [src]

x1 = 1.10714871779409 - 0.712708471535306*i

x2 = 1.10714871779409 + 0.712708471535306*i

x3 = -2.0344439357957 - 0.712708471535306*i

x4 = -2.0344439357957 + 0.712708471535306*i

x4 = -2.0344439357957 + 0.712708471535306*i

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

2*sin(x)^(2)-2*sin(2*x)+5*sin((3*pi/2)-x)^(2)+2=0 la ecuación

Solución numérica:

Solución

2sin(x)^(2)-2sin(2x)+5sin((3*pi/2)-x)^(2)+2=0 la ecuación