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sin(6*x)+sin(2*x)+2*sin(x)^(2)=1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
                           2       
sin(6*x) + sin(2*x) + 2*sin (x) = 1
$$\left(\sin{\left(2 x \right)} + \sin{\left(6 x \right)}\right) + 2 \sin^{2}{\left(x \right)} = 1$$
Gráfica
Respuesta rápida [src]
     -3*pi
x1 = -----
       4  
$$x_{1} = - \frac{3 \pi}{4}$$
     -pi 
x2 = ----
      4  
$$x_{2} = - \frac{\pi}{4}$$
     pi
x3 = --
     4 
$$x_{3} = \frac{\pi}{4}$$
     3*pi
x4 = ----
      4  
$$x_{4} = \frac{3 \pi}{4}$$
x4 = 3*pi/4
Suma y producto de raíces [src]
suma
  3*pi   pi   pi   3*pi
- ---- - -- + -- + ----
   4     4    4     4  
$$\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$
=
0
$$0$$
producto
-3*pi -pi  pi 3*pi
-----*----*--*----
  4    4   4   4  
$$\frac{3 \pi}{4} \frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right)$$
=
    4
9*pi 
-----
 256 
$$\frac{9 \pi^{4}}{256}$$
9*pi^4/256
Respuesta numérica [src]
x1 = -59.5593607243065
x2 = -21.860248881229
x3 = -27.4889357189107
x4 = 10.2101761241668
x5 = -32.2013246992954
x6 = 50.3963821513363
x7 = 55.7632696012188
x8 = -90.9752872602044
x9 = -3.92699081698724
x10 = 7.98488132787406
x11 = 29.9760299030026
x12 = -77.7544181763474
x13 = 3.27249234748937
x14 = 16.4933614313464
x15 = -46.469391334349
x16 = -41.7570023539643
x17 = 66.1043454192852
x18 = -5.49778714378214
x19 = -84.037603483527
x20 = 91.8915851175014
x21 = -55.7632696012188
x22 = 77.7544181763474
x23 = 84.037603483527
x24 = 28.4052335762077
x25 = -76.1836218495525
x26 = 24.2164433714213
x27 = -72.1257313386657
x28 = -95.6876762405891
x29 = 3.92699081698724
x30 = 46.2075919465499
x31 = -25.0018415348188
x32 = 58.2503637853107
x33 = -79.9797129726402
x34 = 2.22529479629277
x35 = -18.0641577581413
x36 = 76.1836218495525
x37 = -94.1168799137942
x38 = 73.9583270532597
x39 = -65.8425460314861
x40 = -40.0553063332699
x41 = 14.2680666350536
x42 = -7.72308194007491
x43 = 33.1176225565924
x44 = -19.7658537788358
x45 = -98.174770424681
x46 = 109.039445018346
x47 = -62.7009533778963
x48 = -48.5637864367422
x49 = -73.6965276654606
x50 = 88.0954939944138
x51 = 40.0553063332699
x52 = -33.7721210260903
x53 = 90.189889096807
x54 = -87.8336946066146
x55 = -57.9885643975116
x56 = -25.9181393921158
x57 = -68.9841386850759
x58 = -14.0062672472545
x59 = 60.3447588877039
x60 = -92.022484811401
x61 = 88.6190927700121
x62 = 25.9181393921158
x63 = -29.7142305152035
x64 = -63.7481509290929
x65 = -43.8513974563575
x66 = 38.3536103125754
x67 = -10.2101761241668
x68 = 68.1987405216784
x69 = -99.7455667514759
x70 = 62.0464549083984
x71 = 0.130899693899575
x72 = 80.2415123604393
x73 = -82.5977068506317
x74 = 18.0641577581413
x75 = 51.9671784781312
x76 = 82.3359074628325
x77 = -70.0313362362725
x78 = -35.997415822383
x79 = -51.705379090332
x80 = -54.1924732744239
x81 = 72.3875307264648
x82 = 44.1131968441567
x83 = 99.7455667514759
x84 = -11.7809724509617
x85 = 11.7809724509617
x86 = -62.0464549083984
x87 = 16.3624617374468
x88 = 69.9004365423729
x89 = 97.5202719551832
x90 = -85.7392995042214
x91 = 53.5379748049261
x92 = 22.1220482690281
x93 = 6.41408500107916
x94 = -2.35619449019234
x95 = -15.5770635740494
x96 = 36.2592152101822
x97 = 33.7721210260903
x98 = 47.9092879672443
x99 = -37.5682121491779
x100 = 94.3786793015934
x101 = 95.9494756283883
x101 = 95.9494756283883