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sin(3*x-pi/6)=(-sqrt(3))/2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
                   ___ 
   /      pi\   -\/ 3  
sin|3*x - --| = -------
   \      6 /      2   
$$\sin{\left(3 x - \frac{\pi}{6} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(3 x - \frac{\pi}{6} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
$$\cos{\left(3 x + \frac{\pi}{3} \right)} = \frac{\sqrt{3}}{2}$$
Esta ecuación se reorganiza en
$$3 x + \frac{\pi}{3} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$3 x + \frac{\pi}{3} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
O
$$3 x + \frac{\pi}{3} = \pi n + \frac{\pi}{6}$$
$$3 x + \frac{\pi}{3} = \pi n - \frac{5 \pi}{6}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{3}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$3 x = \pi n - \frac{\pi}{6}$$
$$3 x = \pi n - \frac{7 \pi}{6}$$
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{18}$$
$$x_{2} = \frac{\pi n}{3} - \frac{7 \pi}{18}$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   pi
- -- + --
  18   2 
$$- \frac{\pi}{18} + \frac{\pi}{2}$$
=
4*pi
----
 9  
$$\frac{4 \pi}{9}$$
producto
-pi  pi
----*--
 18  2 
$$- \frac{\pi}{18} \frac{\pi}{2}$$
=
   2 
-pi  
-----
  36 
$$- \frac{\pi^{2}}{36}$$
-pi^2/36
Respuesta rápida [src]
     -pi 
x1 = ----
      18 
$$x_{1} = - \frac{\pi}{18}$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
x2 = pi/2
Respuesta numérica [src]
x1 = 43.8077642250577
x2 = -75.9218224617533
x3 = -48.3456202802429
x4 = 73.1292956585624
x5 = -0.174532925199433
x6 = -94.4223125328932
x7 = 94.0732466824944
x8 = 89.884456477708
x9 = 81.5068760681352
x10 = 47.9965544298441
x11 = 12.0427718387609
x12 = 8.20304748437335
x13 = 24.60914245312
x14 = 1371.30519329194
x15 = -54.9778714378214
x16 = 26.7035375555132
x17 = 100.007366139275
x18 = -92.3279174305
x19 = 37.5245789178781
x20 = 20.4203522483337
x21 = 58.1194640914112
x22 = -29.845130209103
x23 = 45.9021593274509
x24 = -58.8175957922089
x25 = 66.497044500984
x26 = 75.2236907609556
x27 = -35.7792496658838
x28 = 4.01425727958696
x29 = -52.8834763354282
x30 = 16.2315620435473
x31 = -101.054563690472
x32 = 54.2797397370236
x33 = 79.0634151153431
x34 = 1.91986217719376
x35 = -46.2512251778497
x36 = -4.36332312998582
x37 = 22.5147473507269
x38 = 96.1676417848876
x39 = 41.7133691226645
x40 = 60.2138591938044
x41 = 70.6858347057703
x42 = 68.5914396033772
x43 = 52.1853446346305
x44 = 6.10865238198015
x45 = -39.9680398706701
x46 = 56.025068989018
x47 = -88.1391272257137
x48 = -65.4498469497874
x49 = -44.1568300754565
x50 = 14.1371669411541
x51 = -67.5442420521806
x52 = -42.0624349730633
x53 = -86.0447321233204
x54 = -25.6563400043166
x55 = -2.26892802759263
x56 = -50.4400153826361
x57 = 85.6956662729216
x58 = -78.0162175641465
x59 = 98.2620368872808
x60 = -8.90117918517108
x61 = 83.2522053201295
x62 = -14.8352986419518
x63 = -6.45771823237902
x64 = -17.2787595947439
x65 = -37.873644768277
x66 = -81.8559419185341
x67 = -90.2335223281068
x68 = -282.917871748281
x69 = 87.7900613753148
x70 = -21.4675497995303
x71 = 35.081117965086
x72 = 18.3259571459405
x73 = 83.6012711705284
x74 = -79.7615468161409
x75 = -61.261056745001
x76 = -73.8274273593601
x77 = 39.6189740202713
x78 = 64.4026493985908
x79 = 936.020077844559
x80 = 50.0909495322373
x81 = 91.9788515801012
x82 = 62.3082542961976
x83 = -23.5619449019235
x84 = -83.9503370209273
x85 = -71.733032256967
x86 = 29.1469985083053
x87 = -19.3731546971371
x88 = -69.6386371545737
x89 = -27.7507351067098
x90 = -63.3554518473942
x91 = -31.9395253114962
x92 = -33.6848545634906
x92 = -33.6848545634906