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sin(2*x)+sin(x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(2*x) + sin(x) = 0
$$\sin{\left(x \right)} + \sin{\left(2 x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
  4*pi        2*pi   2*pi        4*pi       
- ---- - pi - ---- + ---- + pi + ---- + 2*pi
   3           3      3           3         
$$\left(\left(\left(\left(\left(- \frac{4 \pi}{3} - \pi\right) - \frac{2 \pi}{3}\right) + \frac{2 \pi}{3}\right) + \pi\right) + \frac{4 \pi}{3}\right) + 2 \pi$$
=
2*pi
$$2 \pi$$
producto
  -4*pi       -2*pi 2*pi    4*pi     
0*-----*(-pi)*-----*----*pi*----*2*pi
    3           3    3       3       
$$2 \pi \frac{4 \pi}{3} \pi \frac{2 \pi}{3} \cdot - \frac{2 \pi}{3} \cdot - \pi 0 \left(- \frac{4 \pi}{3}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -4*pi
x2 = -----
       3  
$$x_{2} = - \frac{4 \pi}{3}$$
x3 = -pi
$$x_{3} = - \pi$$
     -2*pi
x4 = -----
       3  
$$x_{4} = - \frac{2 \pi}{3}$$
     2*pi
x5 = ----
      3  
$$x_{5} = \frac{2 \pi}{3}$$
x6 = pi
$$x_{6} = \pi$$
     4*pi
x7 = ----
      3  
$$x_{7} = \frac{4 \pi}{3}$$
x8 = 2*pi
$$x_{8} = 2 \pi$$
x8 = 2*pi
Respuesta numérica [src]
x1 = 62.8318530717959
x2 = -50.2654824574367
x3 = 85.870199198121
x4 = -23.0383461263252
x5 = 73.3038285837618
x6 = -41.8879020478639
x7 = 79.5870138909414
x8 = -77.4926187885482
x9 = 72.2566310325652
x10 = -43.9822971502571
x11 = -90.0589894029074
x12 = -69.1150383789755
x13 = -37.6991118430775
x14 = 34.5575191894877
x15 = -12.5663706143592
x16 = -94.2477796076938
x17 = 52.3598775598299
x18 = -48.1710873550435
x19 = -14.6607657167524
x20 = -56.5486677646163
x21 = -21.9911485751286
x22 = 50.2654824574367
x23 = -15.707963267949
x24 = -46.0766922526503
x25 = -2.0943951023932
x26 = -5612.97887441376
x27 = 21.9911485751286
x28 = -87.9645943005142
x29 = -73.3038285837618
x30 = -72.2566310325652
x31 = 20.943951023932
x32 = -92.1533845053006
x33 = -52.3598775598299
x34 = -67.0206432765823
x35 = 4.18879020478639
x36 = 59.6902604182061
x37 = 41.8879020478639
x38 = -9.42477796076938
x39 = -85.870199198121
x40 = 31.4159265358979
x41 = 35.6047167406843
x42 = 48.1710873550435
x43 = 10.471975511966
x44 = -35.6047167406843
x45 = -65.9734457253857
x46 = 46.0766922526503
x47 = 15.707963267949
x48 = -83.7758040957278
x49 = 28.2743338823081
x50 = 94.2477796076938
x51 = 39.7935069454707
x52 = -79.5870138909414
x53 = 37.6991118430775
x54 = 96.342174710087
x55 = 6.28318530717959
x56 = -53.4070751110265
x57 = 14.6607657167524
x58 = -58.6430628670095
x59 = 83.7758040957278
x60 = -6.28318530717959
x61 = 8.37758040957278
x62 = -75.398223686155
x63 = -33.5103216382911
x64 = -29.3215314335047
x65 = 64.9262481741891
x66 = 0.0
x67 = -39.7935069454707
x68 = 2.0943951023932
x69 = 54.4542726622231
x70 = -25.1327412287183
x71 = -28.2743338823081
x72 = 81.6814089933346
x73 = 98.4365698124802
x74 = 100.530964914873
x75 = -8.37758040957278
x76 = 78.5398163397448
x77 = 29.3215314335047
x78 = 92.1533845053006
x79 = 12.5663706143592
x80 = 87.9645943005142
x81 = -100.530964914873
x82 = 58.6430628670095
x83 = 18.8495559215388
x84 = 43.9822971502571
x85 = -31.4159265358979
x86 = -81.6814089933346
x87 = 56.5486677646163
x88 = -4.18879020478639
x89 = -59.6902604182061
x90 = 65.9734457253857
x91 = 90.0589894029074
x92 = -96.342174710087
x93 = 75.398223686155
x93 = 75.398223686155