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La ecuación:
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Ecuación (6*x+8)/2+5=5*x/3
Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
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sin(7*x)-sin(x)=O
Expresiones semejantes
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Expresiones con funciones
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Seno sin
Sin2xsinx-cos2xcosx1/2=0
sin(2*x)^2/2+sin(x+3*pi/2)=1
sin(2x)/cos(x)=0
sin(pi+x)^(2)-2*cos(240)-3*sin(7*pi/2)+cos(pi-x)^(2)=0
sin(x)=sqrt(3)/(4)

sin(7*x)-sin(x)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

sin(7*x) - sin(x) = 0

$$- \sin{\left(x \right)} + \sin{\left(7 x \right)} = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

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)      /    ___\\|
0*-----*-----*--*----*|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     /                            /

$$\frac{5 \pi}{8} \frac{\pi}{8} \cdot - \frac{3 \pi}{8} \cdot 0 \left(- \frac{7 \pi}{8}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)$$

$$0$$

Respuesta rápida [src]

x1 = 0

$$x_{1} = 0$$

     -7*pi
x2 = -----
       8

$$x_{2} = - \frac{7 \pi}{8}$$

     -3*pi
x3 = -----
       8

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

     pi
x4 = --
     8

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

     5*pi
x5 = ----
      8

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

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

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

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

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

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

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

               / /     ___________      ___________\ \                            
               | |    /       ___      /       ___ | |                            
               |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\
x9 = -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
               |      ___________      ___________   |     \  2                  /
               |     /       ___      /       ___    |                            
               \   \/  2 - \/ 2   - \/  2 + \/ 2     /

$$x_{9} = - \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$

x9 = -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)

Respuesta numérica [src]

x1 = 78.1471172580461

x2 = 82.0741080750334

x3 = -23.9546439836222

x4 = 20.0276531666349

x5 = 42.0188017417635

x6 = -93.8550805259951

x7 = -43.9822971502571

x8 = 82.7286065445312

x9 = 38.7463093942741

x10 = 28.2743338823081

x11 = -92.2842841992002

x12 = 16.1006623496477

x13 = 56.5486677646163

x14 = 23.0383461263252

x15 = -53.7997741927252

x16 = 37.3064127613788

x17 = -15.707963267949

x18 = -37.6991118430775

x19 = 70.2931356240716

x20 = -71.8639319508665

x21 = -75.7909227678538

x22 = -101.70906215997

x23 = -45.9457925587507

x24 = 65.9734457253857

x25 = -89.9280897090078

x26 = -31.0232274541992

x27 = 96.2112750161874

x28 = 21.9911485751286

x29 = 24.0855436775217

x30 = 7.33038285837618

x31 = -9.8174770424681

x32 = -236.797546264331

x33 = -97.7820713429823

x34 = -65.9734457253857

x35 = 4.18879020478639

x36 = -31.8086256175967

x37 = -17.8023583703422

x38 = 86.0010988920206

x39 = -42.0188017417635

x40 = 21.5984494934298

x41 = -54.4542726622231

x42 = -13.7444678594553

x43 = -5.89048622548086

x44 = 52.2289778659303

x45 = 60.0829594999048

x46 = -20.0276531666349

x47 = 26.1799387799149

x48 = 100.138265833175

x49 = -21.9911485751286

x50 = -27.8816348006094

x51 = -78.9325154214436

x52 = 74.2201264410589

x53 = -49.872783375738

x54 = 34.164820107789

x55 = 92.2842841992002

x56 = -57.7267650097125

x57 = 56.1559686829176

x58 = -1.96349540849362

x59 = -57.5958653158129

x60 = 64.009950316892

x61 = 30.2378292908018

x62 = -48.3019870489431

x63 = -79.717913584841

x64 = 156.686933597791

x65 = -87.9645943005142

x66 = 12.9590696960579

x67 = -28.2743338823081

x68 = 12.1736715326604

x69 = -61.7846555205993

x70 = 6.28318530717959

x71 = 46.0766922526503

x72 = 0.0

x73 = 87.9645943005142

x74 = 43.9822971502571

x75 = -70.2931356240716

x76 = 97.7820713429823

x77 = 80.634211442138

x78 = 2.0943951023932

x79 = 38.0918109247762

x80 = -64.009950316892

x81 = 72.2566310325652

x82 = 90.0589894029074

x83 = 94.2477796076938

x84 = -80.634211442138

x85 = 64.7953484802895

x86 = 8.24668071567321

x87 = -86.0010988920206

x88 = -83.7758040957278

x89 = 68.0678408277789

x90 = 9.42477796076938

x91 = -35.7356164345839

x92 = -39.7935069454707

x93 = -36.5210145979813

x94 = 50.2654824574367

x95 = 75.398223686155

x96 = -67.9369411338793

x96 = -67.9369411338793

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sin(7*x)-sin(x)=0 la ecuación

Solución numérica:

Solución