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sin(3*x-pi/6)=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /      pi\    
sin|3*x - --| = 1
   \      6 /
sin⁡(3x−π6)=1\sin{\left(3 x - \frac{\pi}{6} \right)} = 1
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(3x−π6)=1\sin{\left(3 x - \frac{\pi}{6} \right)} = 1
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
cos⁡(3x+π3)=−1\cos{\left(3 x + \frac{\pi}{3} \right)} = -1
Esta ecuación se reorganiza en
3x+π3=πn+acos⁡(−1)3 x + \frac{\pi}{3} = \pi n + \operatorname{acos}{\left(-1 \right)}
3x+π3=πn−π+acos⁡(−1)3 x + \frac{\pi}{3} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}
O
3x+π3=πn+π3 x + \frac{\pi}{3} = \pi n + \pi
3x+π3=πn3 x + \frac{\pi}{3} = \pi n
, donde n es cualquier número entero
Transportemos
π3\frac{\pi}{3}
al miembro derecho de la ecuación
con el signo opuesto, en total:
3x=πn+2π33 x = \pi n + \frac{2 \pi}{3}
3x=πn−π33 x = \pi n - \frac{\pi}{3}
Dividamos ambos miembros de la ecuación obtenida en
33
obtenemos la respuesta:
x1=πn3+2π9x_{1} = \frac{\pi n}{3} + \frac{2 \pi}{9}
x2=πn3−π9x_{2} = \frac{\pi n}{3} - \frac{\pi}{9}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
2*pi
----
 9
2π9\frac{2 \pi}{9} 
=
2*pi
----
 9
2π9\frac{2 \pi}{9} 
producto
2*pi
----
 9
2π9\frac{2 \pi}{9} 
=
2*pi
----
 9
2π9\frac{2 \pi}{9} 
2*pi/9
Respuesta rápida [src] 
     2*pi
x1 = ----
      9
x1=2π9x_{1} = \frac{2 \pi}{9} 
x1 = 2*pi/9
Respuesta numérica [src] 
x1 = -22.3402142626598
x2 = -93.5496480147495
x3 = 17.4532926597633
x4 = 46.7748238050978
x5 = -72.605696793503
x6 = -20.2458191823057
x7 = 23.7364779731652
x8 = -108.210413790851
x9 = 0.698131538644281
x10 = 38.3972434590332
x11 = 80.2851455676289
x12 = 1215.44729102514
x13 = 59.3411945542951
x14 = 6.98131738963163
x15 = 71.9075652565075
x16 = -83.0776723381025
x17 = -95.6440430738893
x18 = -64.2281163382546
x19 = -13.9626340792321
x20 = 34.2084533743368
x21 = 30.0196631067333
x22 = -3.49065863342137
x23 = -57.9449312887879
x24 = -39.0953752427323
x25 = -72.6056969119452
x26 = -30.7177951259181
x27 = 84.4739356795287
x28 = -91.4552529447199
x29 = -70.5113016254591
x30 = -26.5290044818767
x31 = 82.3795406177083
x32 = -55.8505359402851
x33 = -5.58505369926492
x34 = -51.6617459142679
x35 = 61.4355897989844
x36 = -28.6233996687551
x37 = -47.472955789286
x38 = 48.8692189852738
x39 = 65.624380042164
x40 = 92.8515161116465
x41 = -43.284165610527
x42 = 42.5860335981786
x43 = 44.6804286887779
x44 = 10902.0246395221
x45 = -68.4169065092166
x46 = 25.8308730422062
x47 = -87.2664627585936
x48 = -78.888882234215
x49 = 4.88692186627621
x50 = -1.39626355563388
x51 = 19.5476877895233
x52 = 63.529984937518
x53 = -97.7384381200288
x54 = 88.662725839761
x55 = 32.1140586643481
x56 = 50.9636144224062
x57 = 69.8131701997739
x58 = -16.0570290667896
x59 = -9.77384379218869
x60 = 27.925268095405
x61 = -62.1337212745351
x62 = -41.1897704779514
x63 = -45.3785607088847
x64 = 53.0580092722199
x65 = -7.67944875418476
x66 = 67.7187751281518
x67 = 132.645023597384
x68 = 36.3028484064187
x69 = -53.7561409567887
x70 = 78.1907505437593
x71 = 13.2645019128334
x72 = -66.3225114159317
x73 = -11.8682387751289
x74 = -18.1514241158842
x75 = -89.3608578615271
x76 = 94.9459114679747
x77 = -49.5673508571922
x78 = 86.5683307525137
x79 = -74.7000921670648
x80 = 74.0019602821716
x81 = 21.6420828900494
x82 = -99.8328331263424
x83 = -37.000979782941
x84 = 15.3588974481352
x85 = 40.4916385228553
x86 = 2.79252666236782
x87 = 90.7571209497843
x88 = 57.2467991944529
x89 = -60.0393262304117
x90 = -24.434609359423
x91 = -85.1720676152451
x91 = -85.1720676152451
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