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sin(x)+sin(2*x)+sin(3*x)=0

sin(x)+sin(2*x)+sin(3*x)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sin(x) + sin(2*x) + sin(3*x) = 0
$$\left(\sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \sin{\left(3 x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
  2*pi   pi   pi   2*pi     
- ---- - -- + -- + ---- + pi
   3     2    2     3       
$$\left(\left(\left(- \frac{2 \pi}{3} - \frac{\pi}{2}\right) + \frac{\pi}{2}\right) + \frac{2 \pi}{3}\right) + \pi$$
=
pi
$$\pi$$
producto
  -2*pi -pi  pi 2*pi   
0*-----*----*--*----*pi
    3    2   2   3     
$$\pi \frac{2 \pi}{3} \frac{\pi}{2} \cdot - \frac{\pi}{2} \cdot 0 \left(- \frac{2 \pi}{3}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -2*pi
x2 = -----
       3  
$$x_{2} = - \frac{2 \pi}{3}$$
     -pi 
x3 = ----
      2  
$$x_{3} = - \frac{\pi}{2}$$
     pi
x4 = --
     2 
$$x_{4} = \frac{\pi}{2}$$
     2*pi
x5 = ----
      3  
$$x_{5} = \frac{2 \pi}{3}$$
x6 = pi
$$x_{6} = \pi$$
x6 = pi
Respuesta numérica [src]
x1 = 35.6047167406843
x2 = 100.530964914873
x3 = -34.5575191894877
x4 = -81.6814089933346
x5 = -23.5619449019235
x6 = 65.9734457253857
x7 = 26.7035375555132
x8 = -73.8274273593601
x9 = -43.9822971502571
x10 = 92.1533845053006
x11 = 90.0589894029074
x12 = 78.5398163397448
x13 = -33.5103216382911
x14 = 4.18879020478639
x15 = -77.4926187885482
x16 = -64.4026493985908
x17 = 83.7758040957278
x18 = -31.4159265358979
x19 = -20.4203522483337
x20 = 70.6858347057703
x21 = 21.9911485751286
x22 = -53.4070751110265
x23 = -87.9645943005142
x24 = -67.5442420521806
x25 = 14.1371669411541
x26 = -7.85398163397448
x27 = -86.3937979737193
x28 = 94.2477796076938
x29 = 80.1106126665397
x30 = 2.0943951023932
x31 = 12.5663706143592
x32 = -29.845130209103
x33 = -21.9911485751286
x34 = -15.707963267949
x35 = 54.4542726622231
x36 = -59.6902604182061
x37 = 28.2743338823081
x38 = -75.398223686155
x39 = 14.6607657167524
x40 = 23.5619449019235
x41 = 48.1710873550435
x42 = -65.9734457253857
x43 = 52.3598775598299
x44 = -46.0766922526503
x45 = 15.707963267949
x46 = 79.5870138909414
x47 = -17.2787595947439
x48 = -95.8185759344887
x49 = 56.5486677646163
x50 = 34.5575191894877
x51 = 58.1194640914112
x52 = 29.845130209103
x53 = 72.2566310325652
x54 = 0.0
x55 = 58.6430628670095
x56 = 41.8879020478639
x57 = 10.471975511966
x58 = -92.1533845053006
x59 = 96.342174710087
x60 = 43.9822971502571
x61 = -58.1194640914112
x62 = -48.1710873550435
x63 = -2.0943951023932
x64 = 36.1283155162826
x65 = 87.9645943005142
x66 = 98.4365698124802
x67 = 67.5442420521806
x68 = -114.668131856027
x69 = 59.6902604182061
x70 = -72.2566310325652
x71 = -37.6991118430775
x72 = 39.7935069454707
x73 = -14.1371669411541
x74 = -28.2743338823081
x75 = -85.870199198121
x76 = -79.5870138909414
x77 = -94.2477796076938
x78 = 37.6991118430775
x79 = -3.14159265358979
x80 = -50.2654824574367
x81 = 81.6814089933346
x82 = 84.8230016469244
x83 = -4.18879020478639
x84 = -39.7935069454707
x85 = 50.2654824574367
x86 = -41.8879020478639
x87 = 46.0766922526503
x88 = -61.261056745001
x89 = 20.4203522483337
x90 = -6.28318530717959
x91 = 6.28318530717959
x92 = -51.8362787842316
x93 = 64.4026493985908
x94 = -90.0589894029074
x95 = 73.8274273593601
x96 = -83.7758040957278
x96 = -83.7758040957278
Gráfico
sin(x)+sin(2*x)+sin(3*x)=0 la ecuación