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La ecuación:
Ecuación (x-11)^4=(x+3)^4
Ecuación x^4+2*x^2-8=0
Ecuación x-y=1
Ecuación z^2+3+4*i=0
Expresar {x} en función de y en la ecuación:
-15*x+17*y=13
4*x-7*y=4
-14*x+10*y=19
1*x+6*y=6
Integral de d{x}:
cos(4x)
Derivada de:
cos(4x)
Gráfico de la función y =:
cos(4x)
Expresiones idénticas
sin(7x)-sin(x)=cos(4x)
seno de (7x) menos seno de (x) es igual a coseno de (4x)
sin7x-sinx=cos4x
Expresiones semejantes
d(6x-3cos4x)
cos(4*x)=-1
cos(4*x)=1
sin(7*x)-sin(x)=0
sin(7x)+sin(x)=cos(4x)
sin(7x)-sinx=cos(4x)
Expresiones con funciones
Seno sin
sin(x)=-3/4
sin(x)=-1/5
sin2x=0
sin(3*x-pi/6)=1/2
sin(x)^3+cos(x)^3=1
Seno sin
sin(x)=-3/4
sin(x)=-1/5
sin2x=0
sin(3*x-pi/6)=1/2
sin(x)^3+cos(x)^3=1
Coseno cos
cos(x)=(-1/2)
cos(x)/5=-1
cos(-x)=-1
cos(2x)=1/2
cos(4*x)=1

sin(7x)-sin(x)=cos(4x) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

sin(7*x) - sin(x) = cos(4*x)

- \sin{\left(x \right)} + \sin{\left(7 x \right)} = \cos{\left(4 x \right)}

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     -7*pi
x1 = -----
       8

x_{1} = - \frac{7 \pi}{8}

     -3*pi
x2 = -----
       8

x_{2} = - \frac{3 \pi}{8}

     pi
x3 = --
     8

x_{3} = \frac{\pi}{8}

     5*pi
x4 = ----
      8

x_{4} = \frac{5 \pi}{8}

                                     /   ___________      ___________\
                                     |  /       ___      /       ___ |
       /log(8)      /    ___\\       |\/  2 + \/ 2   + \/  2 - \/ 2  |
x5 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
       \  2                  /       |   ___________      ___________|
                                     |  /       ___      /       ___ |
                                     \\/  2 + \/ 2   - \/  2 - \/ 2  /

x_{5} = \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)

                                     /   ___________      ___________\
                                     |  /       ___      /       ___ |
       /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  |
x6 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
       \  2                  /       |   ___________      ___________|
                                     |  /       ___      /       ___ |
                                     \\/  2 + \/ 2   + \/  2 - \/ 2  /

x_{6} = \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)

                                          /    ___________      ___________ \
                                          |   /       ___      /       ___  |
            /log(8)      /    ___\\       | \/  2 + \/ 2   - \/  2 - \/ 2   |
x7 = pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------|
            \  2                  /       |     ___________      ___________|
                                          |    /       ___      /       ___ |
                                          \- \/  2 + \/ 2   - \/  2 - \/ 2  /

x_{7} = \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)

               / /     ___________      ___________\ \                            
               | |    /       ___      /       ___ | |                            
               |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\
x8 = -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
               |      ___________      ___________   |     \  2                  /
               |     /       ___      /       ___    |                            
               \   \/  2 - \/ 2   - \/  2 + \/ 2     /

x_{8} = - \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)

x8 = -pi - atan(-(-sqrt(sqrt(2) + 2) - sqrt(2 - sqrt(2)))/(-sqrt(sqrt(2) + 2) + sqrt(2 - sqrt(2)))) + i*(-log(2*sqrt(2)) + log(8)/2)

Suma y producto de raíces [src]

suma

                                                            /   ___________      ___________\                                   /   ___________      ___________\                                        /    ___________      ___________ \             / /     ___________      ___________\ \                            
                                                            |  /       ___      /       ___ |                                   |  /       ___      /       ___ |                                        |   /       ___      /       ___  |             | |    /       ___      /       ___ | |                            
  7*pi   3*pi   pi   5*pi     /log(8)      /    ___\\       |\/  2 + \/ 2   + \/  2 - \/ 2  |     /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  |          /log(8)      /    ___\\       | \/  2 + \/ 2   - \/  2 - \/ 2   |             |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\
- ---- - ---- + -- + ---- + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------| + -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
   8      8     8     8       \  2                  /       |   ___________      ___________|     \  2                  /       |   ___________      ___________|          \  2                  /       |     ___________      ___________|             |      ___________      ___________   |     \  2                  /
                                                            |  /       ___      /       ___ |                                   |  /       ___      /       ___ |                                        |    /       ___      /       ___ |             |     /       ___      /       ___    |                            
                                                            \\/  2 + \/ 2   - \/  2 - \/ 2  /                                   \\/  2 + \/ 2   + \/  2 - \/ 2  /                                        \- \/  2 + \/ 2   - \/  2 - \/ 2  /             \   \/  2 - \/ 2   - \/  2 + \/ 2     /

\left(\left(\left(\left(\left(\left(- \frac{7 \pi}{8} - \frac{3 \pi}{8}\right) + \frac{\pi}{8}\right) + \frac{5 \pi}{8}\right) + \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)

      / /     ___________      ___________\ \                                          /   ___________      ___________\       /   ___________      ___________\       /    ___________      ___________ \
      | |    /       ___      /       ___ | |                                          |  /       ___      /       ___ |       |  /       ___      /       ___ |       |   /       ___      /       ___  |
      |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |   pi       /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  |       |\/  2 + \/ 2   + \/  2 - \/ 2  |       | \/  2 + \/ 2   - \/  2 - \/ 2   |
- atan|-------------------------------------| - -- + 4*I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + atan|-------------------------------| + atan|---------------------------------|
      |      ___________      ___________   |   2        \  2                  /       |   ___________      ___________|       |   ___________      ___________|       |     ___________      ___________|
      |     /       ___      /       ___    |                                          |  /       ___      /       ___ |       |  /       ___      /       ___ |       |    /       ___      /       ___ |
      \   \/  2 - \/ 2   - \/  2 + \/ 2     /                                          \\/  2 + \/ 2   + \/  2 - \/ 2  /       \\/  2 + \/ 2   - \/  2 - \/ 2  /       \- \/  2 + \/ 2   - \/  2 - \/ 2  /

- \frac{\pi}{2} + \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + 4 i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)

producto

                    /                                /   ___________      ___________\\ /                                /   ___________      ___________\\ /                                     /    ___________      ___________ \\ /          / /     ___________      ___________\ \                            \
                    |                                |  /       ___      /       ___ || |                                |  /       ___      /       ___ || |                                     |   /       ___      /       ___  || |          | |    /       ___      /       ___ | |                            |
-7*pi -3*pi pi 5*pi |  /log(8)      /    ___\\       |\/  2 + \/ 2   + \/  2 - \/ 2  || |  /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  || |       /log(8)      /    ___\\       | \/  2 + \/ 2   - \/  2 - \/ 2   || |          |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\|
-----*-----*--*----*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------||*|-pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /||
  8     8   8   8   |  \  2                  /       |   ___________      ___________|| |  \  2                  /       |   ___________      ___________|| |       \  2                  /       |     ___________      ___________|| |          |      ___________      ___________   |     \  2                  /|
                    |                                |  /       ___      /       ___ || |                                |  /       ___      /       ___ || |                                     |    /       ___      /       ___ || |          |     /       ___      /       ___    |                            |
                    \                                \\/  2 + \/ 2   - \/  2 - \/ 2  // \                                \\/  2 + \/ 2   + \/  2 - \/ 2  // \                                     \- \/  2 + \/ 2   - \/  2 - \/ 2  // \          \   \/  2 - \/ 2   - \/  2 + \/ 2     /                            /

\frac{5 \pi}{8} \frac{\pi}{8} \cdot - \frac{7 \pi}{8} \left(- \frac{3 \pi}{8}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)

        /         /   ___________      ___________\\ /         /   ___________      ___________\\     /   ___________      ___________\     /   ___________      ___________\
        |         |  /       ___      /       ___ || |         |  /       ___      /       ___ ||     |  /       ___      /       ___ |     |  /       ___      /       ___ |
      4 |         |\/  2 - \/ 2   - \/  2 + \/ 2  || |         |\/  2 + \/ 2   + \/  2 - \/ 2  ||     |\/  2 - \/ 2   - \/  2 + \/ 2  |     |\/  2 + \/ 2   + \/  2 - \/ 2  |
105*pi *|pi + atan|-------------------------------||*|pi + atan|-------------------------------||*atan|-------------------------------|*atan|-------------------------------|
        |         |   ___________      ___________|| |         |   ___________      ___________||     |   ___________      ___________|     |   ___________      ___________|
        |         |  /       ___      /       ___ || |         |  /       ___      /       ___ ||     |  /       ___      /       ___ |     |  /       ___      /       ___ |
        \         \\/  2 + \/ 2   + \/  2 - \/ 2  // \         \\/  2 - \/ 2   - \/  2 + \/ 2  //     \\/  2 + \/ 2   + \/  2 - \/ 2  /     \\/  2 - \/ 2   - \/  2 + \/ 2  /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     4096

\frac{105 \pi^{4} \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \pi\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \pi\right) \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)}}{4096}

105*pi^4*(pi + atan((sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))/(sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))))*(pi + atan((sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))/(sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))))*atan((sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))/(sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2))))*atan((sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))/(sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2))))/4096

Respuesta numérica [src]

x1 = 90.2335223281068

x2 = 78.1471172580461

x3 = 88.1391272257137

x4 = -98.5674695063798

x5 = 82.0741080750334

x6 = -23.9546439836222

x7 = 20.0276531666349

x8 = -17.9768912955416

x9 = 42.0188017417635

x10 = 96.5167076352864

x11 = -93.8550805259951

x12 = 2.26892802759263

x13 = 23.9546439836222

x14 = 32.2885911618951

x15 = -96.9966731795849

x16 = 16.1006623496477

x17 = -53.7997741927252

x18 = 4.31968989868597

x19 = 39.9680398706701

x20 = 9.03207887907065

x21 = 41.233403578366

x22 = -66.3661448070844

x23 = -71.8639319508665

x24 = 28.0998009571087

x25 = 71.8639319508665

x26 = -75.7909227678538

x27 = -82.0741080750334

x28 = -75.0055246044563

x29 = 10.6465084371654

x30 = 96.2112750161874

x31 = -22.165681500328

x32 = -9.8174770424681

x33 = -97.7820713429823

x34 = -31.8086256175967

x35 = 69.9877030049726

x36 = 86.0010988920206

x37 = 83.9503370209273

x38 = -42.0188017417635

x39 = -87.7900613753148

x40 = -13.7444678594553

x41 = -5.89048622548086

x42 = 29.4524311274043

x43 = 26.0054058547155

x44 = 52.2289778659303

x45 = -43.8077642250577

x46 = 60.0829594999048

x47 = -4.01425727958696

x48 = -20.0276531666349

x49 = 100.138265833175

x50 = -27.8816348006094

x51 = -78.9325154214436

x52 = 67.9369411338793

x53 = -31.2413936106985

x54 = -78.7143492649443

x55 = 74.2201264410589

x56 = -49.872783375738

x57 = 34.164820107789

x58 = 92.2842841992002

x59 = 53.0143760293278

x60 = -59.8647933434055

x61 = 56.1559686829176

x62 = 65.5807466436869

x63 = -1.96349540849362

x64 = -11.693705988362

x65 = 64.009950316892

x66 = 46.2512251778497

x67 = -8.24668071567321

x68 = -61.9591884457987

x69 = 76.2708883121522

x70 = 30.2378292908018

x71 = -79.717913584841

x72 = -55.3705705195201

x73 = 12.1736715326604

x74 = 102.799892942466

x75 = -57.7703982410123

x76 = 0.174532925199433

x77 = -91.9788515801012

x78 = 38.0918109247762

x79 = -64.009950316892

x80 = -88.3572933822129

x81 = 44.1568300754565

x82 = -34.9502182711865

x83 = 48.3019870489431

x84 = 72.0820981073658

x85 = 64.7953484802895

x86 = 8.24668071567321

x87 = 14.5298660228528

x88 = -15.8824961931484

x89 = -86.0010988920206

x90 = -98.2620368872808

x91 = -39.6626072515711

x92 = -47.9965544298441

x93 = -35.7356164345839

x94 = -83.6449044018282

x95 = -67.9369411338793

x95 = -67.9369411338793

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

sin(7x)-sin(x)=cos(4x) la ecuación

Solución numérica:

Solución