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sin(4*x)-sin(x)=0

sin(4*x)-sin(x)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sin(4*x) - sin(x) = 0
$$- \sin{\left(x \right)} + \sin{\left(4 x \right)} = 0$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -9*pi
x2 = -----
       5  
$$x_{2} = - \frac{9 \pi}{5}$$
x3 = -pi
$$x_{3} = - \pi$$
     pi
x4 = --
     5 
$$x_{4} = \frac{\pi}{5}$$
x5 = pi
$$x_{5} = \pi$$
             /              ___________                      ___________\
             |      ____   /       ___        ___     ___   /       ___ |
             |I   \/ 10 *\/  5 + \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5  |
x6 = -2*I*log|- - --------------------- + ------- + --------------------|
             \4             8                4               8          /
$$x_{6} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
             /                         ___________             ___________\
             |          ___     ___   /       ___      ____   /       ___ |
             |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5  |
x7 = -2*I*log|- - - ------- - -------------------- + ---------------------|
             \  4      4               8                       8          /
$$x_{7} = - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
             /              ___________                      ___________            ___________             ___________\
             |      ____   /       ___        ___     ___   /       ___      ___   /       ___      ____   /       ___ |
             |I   \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5  |
x8 = -2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------|
             \4             16               4               16                     16                      16         /
$$x_{8} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
             /               ___________             ___________             ___________                      ___________\
             |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |
             |  I   \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 - \/ 5  |
x9 = -2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
             \  4            16                      16                      16               4               16         /
$$x_{9} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
              /                         ___________            ___________             ___________             ___________\
              |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |
              |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |
x10 = -2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
              \  4      4               16                     16                      16                      16         /
$$x_{10} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
              /                       ___________            ___________             ___________             ___________\
              |        ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |
              |I   I*\/ 5    \/ 2 *\/  5 - \/ 5     \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |
x11 = -2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------|
              \4      4               16                     16                      16                      16         /
$$x_{11} = - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)}$$
x11 = -2*i*log(-sqrt(2)*sqrt(5 - sqrt(5))/16 + sqrt(2)*sqrt(sqrt(5) + 5)/16 + sqrt(10)*sqrt(5 - sqrt(5))/16 + sqrt(10)*sqrt(sqrt(5) + 5)/16 - sqrt(5)*i/4 + i/4)
Suma y producto de raíces [src]
suma
                               /              ___________                      ___________\          /                         ___________             ___________\          /              ___________                      ___________            ___________             ___________\          /               ___________             ___________             ___________                      ___________\          /                         ___________            ___________             ___________             ___________\          /                       ___________            ___________             ___________             ___________\
                               |      ____   /       ___        ___     ___   /       ___ |          |          ___     ___   /       ___      ____   /       ___ |          |      ____   /       ___        ___     ___   /       ___      ___   /       ___      ____   /       ___ |          |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |          |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |          |        ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |
  9*pi        pi               |I   \/ 10 *\/  5 + \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5  |          |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5  |          |I   \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5  |          |  I   \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 - \/ 5  |          |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |          |I   I*\/ 5    \/ 2 *\/  5 - \/ 5     \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |
- ---- - pi + -- + pi - 2*I*log|- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- + ---------------------| - 2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------| - 2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - 2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------|
   5          5                \4             8                4               8          /          \  4      4               8                       8          /          \4             16               4               16                     16                      16         /          \  4            16                      16                      16               4               16         /          \  4      4               16                     16                      16                      16         /          \4      4               16                     16                      16                      16         /
$$- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)} + \left(- 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(\left(- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(\left(\left(- \frac{9 \pi}{5} - \pi\right) + \frac{\pi}{5}\right) + \pi\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right)\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right)\right)$$
=
                /                         ___________             ___________\          /              ___________                      ___________\          /                         ___________            ___________             ___________             ___________\          /               ___________             ___________             ___________                      ___________\          /                       ___________            ___________             ___________             ___________\          /              ___________                      ___________            ___________             ___________\
                |          ___     ___   /       ___      ____   /       ___ |          |      ____   /       ___        ___     ___   /       ___ |          |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |          |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |          |        ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |          |      ____   /       ___        ___     ___   /       ___      ___   /       ___      ____   /       ___ |
  8*pi          |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5  |          |I   \/ 10 *\/  5 + \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5  |          |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |          |  I   \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 - \/ 5  |          |I   I*\/ 5    \/ 2 *\/  5 - \/ 5     \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |          |I   \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5  |
- ---- - 2*I*log|- - - ------- - -------------------- + ---------------------| - 2*I*log|- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - 2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - 2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------| - 2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------|
   5            \  4      4               8                       8          /          \4             8                4               8          /          \  4      4               16                     16                      16                      16         /          \  4            16                      16                      16               4               16         /          \4      4               16                     16                      16                      16         /          \4             16               4               16                     16                      16         /
$$- \frac{8 \pi}{5} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
producto
                            /              ___________                      ___________\         /                         ___________             ___________\         /              ___________                      ___________            ___________             ___________\         /               ___________             ___________             ___________                      ___________\         /                         ___________            ___________             ___________             ___________\         /                       ___________            ___________             ___________             ___________\
                            |      ____   /       ___        ___     ___   /       ___ |         |          ___     ___   /       ___      ____   /       ___ |         |      ____   /       ___        ___     ___   /       ___      ___   /       ___      ____   /       ___ |         |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |         |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |         |        ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |
  -9*pi       pi            |I   \/ 10 *\/  5 + \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5  |         |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5  |         |I   \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5  |         |  I   \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 - \/ 5  |         |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |         |I   I*\/ 5    \/ 2 *\/  5 - \/ 5     \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5  |
0*-----*(-pi)*--*pi*-2*I*log|- - --------------------- + ------- + --------------------|*-2*I*log|- - - ------- - -------------------- + ---------------------|*-2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------|*-2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|*-2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|*-2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------|
    5         5             \4             8                4               8          /         \  4      4               8                       8          /         \4             16               4               16                     16                      16         /         \  4            16                      16                      16               4               16         /         \  4      4               16                     16                      16                      16         /         \4      4               16                     16                      16                      16         /
$$- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} \pi \frac{\pi}{5} \cdot - \pi 0 \left(- \frac{9 \pi}{5}\right)$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = -29.5309709437441
x2 = -49.6371639267187
x3 = 18.8495559215388
x4 = 86.0796387083603
x5 = -58.6430628670095
x6 = 96.1327351998477
x7 = -81.6814089933346
x8 = -19.4778744522567
x9 = 65.9734457253857
x10 = 357.513243978518
x11 = -43.9822971502571
x12 = 18.2212373908208
x13 = 92.1533845053006
x14 = -8.16814089933346
x15 = 90.0589894029074
x16 = -56.5486677646163
x17 = -33.5103216382911
x18 = 4.18879020478639
x19 = -77.4926187885482
x20 = 52.1504380495906
x21 = 83.7758040957278
x22 = 64.7168086639497
x23 = 68.4867198482575
x24 = 42.0973415581032
x25 = 21.9911485751286
x26 = -96.1327351998477
x27 = -87.9645943005142
x28 = 94.2477796076938
x29 = -73.5132680940012
x30 = 2.0943951023932
x31 = -93.6194610769758
x32 = 14.451326206513
x33 = -45.867252742411
x34 = 58.4336233567702
x35 = 62.2035345410779
x36 = 55.9203492338983
x37 = -21.9911485751286
x38 = -69.7433569096934
x39 = -15.707963267949
x40 = -100.530964914873
x41 = 54.4542726622231
x42 = -59.6902604182061
x43 = 28.2743338823081
x44 = -5.65486677646163
x45 = 8.16814089933346
x46 = -18.2212373908208
x47 = 69.7433569096934
x48 = -62.2035345410779
x49 = 35.8141562509236
x50 = 48.1710873550435
x51 = 32.0442450666159
x52 = -65.9734457253857
x53 = -79.7964534011807
x54 = -25.7610597594363
x55 = -63.4601716025138
x56 = 38.3274303737955
x57 = 72.2566310325652
x58 = 11.9380520836412
x59 = 0.0
x60 = -64.9262481741891
x61 = -55.9203492338983
x62 = 10.471975511966
x63 = -92.1533845053006
x64 = 43.9822971502571
x65 = -89.8495498926681
x66 = -48.1710873550435
x67 = 87.9645943005142
x68 = 98.4365698124802
x69 = -1.88495559215388
x70 = -37.6991118430775
x71 = 39.7935069454707
x72 = -52.1504380495906
x73 = -85.870199198121
x74 = 24.5044226980004
x75 = 69.1150383789755
x76 = -35.8141562509236
x77 = -76.026542216873
x78 = 79.7964534011807
x79 = 37.6991118430775
x80 = 94.8760981384118
x81 = -4.18879020478639
x82 = -39.7935069454707
x83 = 50.2654824574367
x84 = -41.8879020478639
x85 = 46.0766922526503
x86 = -32.0442450666159
x87 = 6.28318530717959
x88 = 82.3097275240526
x89 = 25.7610597594363
x90 = -83.7758040957278
x91 = 99.9026463841554
x92 = -11.9380520836412
x93 = 76.026542216873
x94 = -99.9026463841554
x94 = -99.9026463841554
Gráfico
sin(4*x)-sin(x)=0 la ecuación