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cos(x)+sin(3x)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(x) + sin(3*x) = 0
$$\sin{\left(3 x \right)} + \cos{\left(x \right)} = 0$$
Gráfica
Respuesta rápida [src]
     -5*pi
x1 = -----
       8  
$$x_{1} = - \frac{5 \pi}{8}$$
     -pi 
x2 = ----
      4  
$$x_{2} = - \frac{\pi}{4}$$
     -pi 
x3 = ----
      8  
$$x_{3} = - \frac{\pi}{8}$$
     3*pi
x4 = ----
      8  
$$x_{4} = \frac{3 \pi}{8}$$
     3*pi
x5 = ----
      4  
$$x_{5} = \frac{3 \pi}{4}$$
     7*pi
x6 = ----
      8  
$$x_{6} = \frac{7 \pi}{8}$$
x6 = 7*pi/8
Suma y producto de raíces [src]
suma
  5*pi   pi   pi   3*pi   3*pi   7*pi
- ---- - -- - -- + ---- + ---- + ----
   8     4    8     8      4      8  
$$\left(\left(\left(\left(- \frac{5 \pi}{8} - \frac{\pi}{4}\right) - \frac{\pi}{8}\right) + \frac{3 \pi}{8}\right) + \frac{3 \pi}{4}\right) + \frac{7 \pi}{8}$$
=
pi
$$\pi$$
producto
-5*pi -pi  -pi  3*pi 3*pi 7*pi
-----*----*----*----*----*----
  8    4    8    8    4    8  
$$\frac{7 \pi}{8} \frac{3 \pi}{4} \frac{3 \pi}{8} \cdot - \frac{\pi}{8} \cdot - \frac{5 \pi}{8} \left(- \frac{\pi}{4}\right)$$
=
       6
-315*pi 
--------
 65536  
$$- \frac{315 \pi^{6}}{65536}$$
-315*pi^6/65536
Respuesta numérica [src]
x1 = 18.0641577581413
x2 = 52.621676947629
x3 = 48.3019870489431
x4 = 33.7721210260903
x5 = -74.2201264410589
x6 = 26.3108384738145
x7 = -89.9280897090078
x8 = -66.3661448070844
x9 = -69.9004365423729
x10 = 46.3384916404494
x11 = -23.9546439836222
x12 = -82.0741080750334
x13 = -60.0829594999048
x14 = -99.3528676697772
x15 = 43.5895980685584
x16 = -98.174770424681
x17 = -7.06858347057703
x18 = 30.6305283725005
x19 = 71.8639319508665
x20 = -9.8174770424681
x21 = -91.8915851175014
x22 = 87.5718952188155
x23 = -52.2289778659303
x24 = 53.0143760293278
x25 = -17.6714586764426
x26 = -38.0918109247762
x27 = -78.9325154214436
x28 = 78.1471172580461
x29 = 5.89048622548086
x30 = 64.009950316892
x31 = -33.3794219443916
x32 = -19.6349540849362
x33 = 68.329640215578
x34 = -56.941366846315
x35 = -96.2112750161874
x36 = 27.8816348006094
x37 = -61.6537558266997
x38 = -44.3749962319558
x39 = -77.3617190946487
x40 = -85.6083998103219
x41 = -47.9092879672443
x42 = -8.24668071567321
x43 = -11.388273369263
x44 = 40.0553063332699
x45 = 57.7267650097125
x46 = 42.0188017417635
x47 = 56.1559686829176
x48 = 9.03207887907065
x49 = 100.138265833175
x50 = 67.1515429704818
x51 = 86.0010988920206
x52 = 24.3473430653209
x53 = -25.9181393921158
x54 = 98.5674695063798
x55 = -16.1006623496477
x56 = -39.6626072515711
x57 = 79.717913584841
x58 = 90.3207887907066
x59 = -22.3838476568273
x60 = -53.7997741927252
x61 = 49.872783375738
x62 = -3.92699081698724
x63 = 76.5763209312512
x64 = 65.5807466436869
x65 = 35.7356164345839
x66 = 20.0276531666349
x67 = -45.9457925587507
x68 = -75.7909227678538
x69 = -67.9369411338793
x70 = 21.5984494934298
x71 = -30.2378292908018
x72 = -31.8086256175967
x73 = -41.6261026600648
x74 = 70.2931356240716
x75 = 2.35619449019234
x76 = 12.1736715326604
x77 = -0.392699081698724
x78 = 4.31968989868597
x79 = -97.7820713429823
x80 = -83.6449044018282
x81 = 32.5940237809941
x82 = 74.6128255227576
x83 = -1.96349540849362
x84 = 34.164820107789
x85 = -34.9502182711865
x86 = -88.3572933822129
x87 = -55.3705705195201
x88 = 93.8550805259951
x89 = -12.9590696960579
x90 = 62.0464549083984
x91 = 92.2842841992002
x92 = 13.7444678594553
x93 = 54.5851723561227
x94 = 96.6039740978861
x95 = -63.6172512351933
x96 = 10.6028752058656
x97 = 84.037603483527
x97 = 84.037603483527