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sin(2x)+sin(pi-8x)=sqrt(2)*cos(3x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                             ___         
sin(2*x) + sin(pi - 8*x) = \/ 2 *cos(3*x)
$$\sin{\left(2 x \right)} + \sin{\left(\pi - 8 x \right)} = \sqrt{2} \cos{\left(3 x \right)}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -5*pi
x1 = -----
       6
$$x_{1} = - \frac{5 \pi}{6}$$ 
     -pi 
x2 = ----
      2
$$x_{2} = - \frac{\pi}{2}$$ 
     -pi 
x3 = ----
      6
$$x_{3} = - \frac{\pi}{6}$$ 
     pi
x4 = --
     6
$$x_{4} = \frac{\pi}{6}$$ 
     pi
x5 = --
     2
$$x_{5} = \frac{\pi}{2}$$ 
     5*pi
x6 = ----
      6
$$x_{6} = \frac{5 \pi}{6}$$ 
x6 = 5*pi/6
Suma y producto de raíces [src] 
suma
  5*pi   pi   pi   pi   pi   5*pi
- ---- - -- - -- + -- + -- + ----
   6     2    6    6    2     6
$$\left(\left(\left(\left(- \frac{5 \pi}{6} - \frac{\pi}{2}\right) - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{\pi}{2}\right) + \frac{5 \pi}{6}$$ 
=
0
$$0$$ 
producto
-5*pi -pi  -pi  pi pi 5*pi
-----*----*----*--*--*----
  6    2    6   6  2   6
$$\frac{5 \pi}{6} \frac{\pi}{2} \frac{\pi}{6} \cdot - \frac{\pi}{6} \cdot - \frac{5 \pi}{6} \left(- \frac{\pi}{2}\right)$$ 
=
      6
-25*pi 
-------
  5184
$$- \frac{25 \pi^{6}}{5184}$$ 
-25*pi^6/5184
Respuesta numérica [src] 
x1 = -12.0427718387609
x2 = -73.6703477266806
x3 = -88.7499924639117
x4 = 96.9181333632451
x5 = -19.9491133502952
x6 = 95.9756555671682
x7 = 88.1216739331937
x8 = -25.9181393921158
x9 = 44.1393767829366
x10 = 36.1283155162826
x11 = -90.0066295253476
x12 = 23.5619449019235
x13 = -5.75958653158129
x14 = 4.24115008234622
x15 = -69.9004365423729
x16 = -95.8185759344887
x17 = 18.0641577581413
x18 = 60.2138591938044
x19 = 0.15707963267949
x20 = -67.70132168486
x21 = 71.733032256967
x22 = 51.9933584169111
x23 = -43.8252175175776
x24 = -30.0022098417825
x25 = -22.148228207808
x26 = -86.3937979737193
x27 = 31.9395253114962
x28 = -33.7721210260903
x29 = 12.0427718387609
x30 = 21.5199096770901
x31 = 84.2994028713261
x32 = 78.0162175641465
x33 = -77.4402589109884
x34 = -3.66519142918809
x35 = -66.1305253580651
x36 = 10.2101761241668
x37 = -79.9535330338602
x38 = 20.2632726156542
x39 = -27.7507351067098
x40 = 100.007366139275
x41 = -56.025068989018
x42 = -51.8362787842316
x43 = 58.1194640914112
x44 = 6.44026493985908
x45 = 98.174770424681
x46 = 75.9218224617533
x47 = 65.5022068273472
x48 = 80.1106126665397
x49 = -49.7418836818384
x50 = -87.8075146678347
x51 = 74.2986662573986
x52 = 41.9402619254237
x53 = -71.733032256967
x54 = 16.2315620435473
x55 = -100.007366139275
x56 = -31.9395253114962
x57 = 38.2227106186758
x58 = -111.369459569758
x59 = 8.01106126665397
x60 = -59.8473400508856
x61 = 46.6526509058084
x62 = 26.5464579228338
x63 = -38.7986692718339
x64 = -2.04203522483337
x65 = 62.3082542961976
x66 = 0.471238898038469
x67 = 72.0995513998858
x68 = -15.8650429006285
x69 = -39.7411470679109
x70 = -7.85398163397448
x71 = 82.2050077689329
x72 = -19.6349540849362
x73 = -96.2898148325272
x74 = 28.1172542496287
x75 = -57.0722665402146
x76 = -77.7544181763474
x77 = -9.58185759344887
x78 = -46.0243323750905
x79 = 48.2234472326033
x80 = -75.9218224617533
x81 = -93.7765407096553
x82 = 92.2057443828604
x83 = -91.6297857297023
x84 = 14.1371669411541
x85 = -16.2315620435473
x86 = 34.0862802914493
x87 = 64.2455697659113
x88 = 40.317105721069
x89 = 54.1924732744239
x90 = -42.5685804561417
x91 = -47.6474885794452
x92 = 6.80678408277789
x93 = -23.7190245346029
x94 = -63.9314105005523
x95 = 50.7367213554752
x96 = 30.3163691071415
x97 = -63.3554518473942
x98 = 67.0730031541421
x99 = -35.9712358836031
x100 = 56.025068989018
x101 = 85.9225590756809
x101 = 85.9225590756809
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