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cos(3*x-pi*1/6)+1=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /      pi\        
cos|3*x - --| + 1 = 0
   \      6 /        
$$\cos{\left(3 x - \frac{\pi}{6} \right)} + 1 = 0$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(3 x - \frac{\pi}{6} \right)} + 1 = 0$$
es la ecuación trigonométrica más simple
Transportemos 1 al miembro derecho de la ecuación

cambiando el signo de 1

Obtenemos:
$$\cos{\left(3 x - \frac{\pi}{6} \right)} = -1$$
Esta ecuación se reorganiza en
$$3 x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$3 x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
O
$$3 x + \frac{\pi}{3} = 2 \pi n - \frac{\pi}{2}$$
$$3 x + \frac{\pi}{3} = 2 \pi n + \frac{3 \pi}{2}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{3}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$3 x = 2 \pi n - \frac{5 \pi}{6}$$
$$3 x = 2 \pi n + \frac{7 \pi}{6}$$
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} - \frac{5 \pi}{18}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{7 \pi}{18}$$
Gráfica
Respuesta rápida [src]
     -5*pi
x1 = -----
       18 
$$x_{1} = - \frac{5 \pi}{18}$$
     7*pi
x2 = ----
      18 
$$x_{2} = \frac{7 \pi}{18}$$
x2 = 7*pi/18
Suma y producto de raíces [src]
suma
  5*pi   7*pi
- ---- + ----
   18     18 
$$- \frac{5 \pi}{18} + \frac{7 \pi}{18}$$
=
pi
--
9 
$$\frac{\pi}{9}$$
producto
-5*pi 7*pi
-----*----
  18   18 
$$- \frac{5 \pi}{18} \frac{7 \pi}{18}$$
=
      2
-35*pi 
-------
  324  
$$- \frac{35 \pi^{2}}{324}$$
-35*pi^2/324
Respuesta numérica [src]
x1 = -38.5717763457435
x2 = -11.3446402989838
x3 = -15.5334304569628
x4 = -34.3829860965224
x5 = -65.7989127573927
x6 = -9.25024519131613
x7 = 59.8647934405955
x8 = -78.3652832483785
x9 = 76.6199540057474
x10 = -32.2885910093003
x11 = -99.3092346007921
x12 = 49.3928179190077
x13 = -17.6278255179502
x14 = 99.6583004519716
x15 = 9.59931105468093
x16 = 61.9591884851797
x17 = 24.2600765954214
x18 = 11.6937061449814
x19 = -21.8166155863094
x20 = 66.1479787777296
x21 = -84.6484687079856
x22 = 64.0535834321834
x23 = -74.1764930939651
x24 = -46.9493571911488
x25 = -111.875605149508
x26 = 93.3751150431847
x27 = 43.1096329349692
x28 = 3.31612547660458
x29 = -57.4213325394611
x30 = -59.5157276137974
x31 = 95.4695102318843
x32 = 5.41052078886955
x33 = -86.7428642451346
x34 = -53.2325423367113
x35 = 38.920842341877
x36 = 82.9031394677449
x37 = 17.9768913197771
x38 = -76.2708881640826
x39 = -93.0260487973651
x40 = -97.2148394803031
x41 = -5.06145470762809
x42 = -13.4390353849187
x43 = -69.9877030211599
x44 = 57.7703983766449
x45 = -40.6661716073838
x46 = 84.9975349569597
x47 = -61.6101226767856
x48 = 38.9208423710609
x49 = 78.7143491037453
x50 = 13.7881012202592
x51 = 70.3367688009418
x52 = -80.4596783505706
x53 = -55.3269374502927
x54 = -28.0998008785227
x55 = 72.4311638578408
x56 = -82.5540734837771
x57 = 30.543261770101
x58 = 7.50491594339682
x59 = 15.8824962813824
x60 = -26.0054058484444
x61 = -38.5717762514735
x62 = 28.4488667002524
x63 = 3.31612609210568
x64 = 32.637656853052
x65 = 74.5255589255718
x66 = -95.120444287049
x67 = -7.15585003585318
x68 = -51.138147164715
x69 = -19.7222205668814
x70 = 97.5639053549045
x71 = 68.24237375876
x72 = 55.6760032987458
x73 = -36.4773812030096
x74 = 91.280719578531
x75 = 80.808744235512
x76 = -30.1941959366071
x77 = 26.3544716412833
x78 = 22.1656815906139
x79 = 51.4872130884499
x80 = -63.7045177283788
x81 = 36.8264470979358
x82 = -49.0437517633446
x83 = 20.0712861640354
x84 = -72.0820980392391
x85 = 34.7320519555797
x86 = 47.2984225390473
x87 = 53.5816082051786
x87 = 53.5816082051786