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cos(3x)=-1/2

cos(3x)=-1/2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
cos(3*x) = -1/2
$$\cos{\left(3 x \right)} = - \frac{1}{2}$$
Simplificar
Solución detallada
Tenemos la ecuación
$$\cos{\left(3 x \right)} = - \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
O
$$3 x = \pi n + \frac{2 \pi}{3}$$
$$3 x = \pi n - \frac{\pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} + \frac{2 \pi}{9}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{9}$$
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
2*pi   4*pi
---- + ----
 9      9
$$\frac{2 \pi}{9} + \frac{4 \pi}{9}$$ 
=
2*pi
----
 3
$$\frac{2 \pi}{3}$$ 
producto
2*pi 4*pi
----*----
 9    9
$$\frac{2 \pi}{9} \frac{4 \pi}{9}$$ 
=
    2
8*pi 
-----
  81
$$\frac{8 \pi^{2}}{81}$$ 
8*pi^2/81
Respuesta rápida [src] 
     2*pi
x1 = ----
      9
$$x_{1} = \frac{2 \pi}{9}$$ 
     4*pi
x2 = ----
      9
$$x_{2} = \frac{4 \pi}{9}$$ 
x2 = 4*pi/9
Respuesta numérica [src] 
x1 = 44.6804288510548
x2 = 84.4739357965256
x3 = -55.8505360638185
x4 = 20.2458193231342
x5 = 74.0019602845596
x6 = -82.3795406941324
x7 = 69.8131700797732
x8 = -13.9626340159546
x9 = -7.67944870877505
x10 = 87.2664625997165
x11 = -71.9075651821664
x12 = -95.6440430092893
x13 = -76.0963553869528
x14 = 40.4916386462684
x15 = -34.2084533390889
x16 = -93.5496479068961
x17 = 86.5683308989187
x18 = 24.4346095279206
x19 = -49.567350756639
x20 = 57.9449311662117
x21 = 38.3972435438752
x22 = 97.7384381116825
x23 = 27.9252680319093
x24 = 1.39626340159546
x25 = -91.4552528045029
x26 = -25.8308729295161
x27 = -11.8682389135614
x28 = -36.3028484414821
x29 = -51.6617458590322
x30 = 6.98131700797732
x31 = -27.9252680319093
x32 = -30.0196631343025
x33 = 62.1337213709981
x34 = 76.0963553869528
x35 = 18.151424220741
x36 = 13.9626340159546
x37 = -9.77384381116824
x38 = -97.7384381116825
x39 = 42.5860337486616
x40 = 99.8328332140756
x41 = 49.567350756639
x42 = 88.6627260013119
x43 = -67.71877497738
x44 = -53.7561409614254
x45 = -21.6420827247297
x46 = 66.3225115757845
x47 = 30.0196631343025
x48 = 11.8682389135614
x49 = 78.190750489346
x50 = -57.9449311662117
x51 = -65.6243798749868
x52 = -74.0019602845596
x53 = 92.8515162060983
x54 = 22.3402144255274
x55 = -41.1897703470662
x56 = 32.1140582366957
x57 = -247.836753783195
x58 = -80.2851455917392
x59 = 4.88692190558412
x60 = 55.8505360638185
x61 = -89.3608577021097
x62 = 9.77384381116824
x63 = 34.2084533390889
x64 = -5.58505360638185
x65 = -32.1140582366957
x66 = 16.0570291183478
x67 = -62.1337213709981
x68 = 82.3795406941324
x69 = -3.49065850398866
x70 = -99.8328332140756
x71 = 64.2281164733913
x72 = 7.67944870877505
x73 = 36.3028484414821
x74 = -1.39626340159546
x75 = -78.190750489346
x76 = -45.3785605518526
x77 = 71.9075651821664
x78 = -47.4729556542458
x79 = -69.8131700797732
x80 = -16.0570291183478
x81 = 53.7561409614254
x82 = 60.0393262686049
x83 = -23.7364778271229
x84 = 68.4169066781777
x85 = -38.3972435438752
x86 = 48.8692190558412
x87 = 95.6440430092893
x88 = 80.2851455917392
x89 = -18.151424220741
x90 = 25.8308729295161
x91 = -60.0393262686049
x92 = 51.6617458590322
x93 = 45.3785605518526
x93 = 45.3785605518526
Gráfico
cos(3x)=-1/2 la ecuación
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