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sin(2*x-pi/3)=0

sin(2*x-pi/3)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /      pi\    
sin|2*x - --| = 0
   \      3 /
sin⁡(2x−π3)=0\sin{\left(2 x - \frac{\pi}{3} \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(2x−π3)=0\sin{\left(2 x - \frac{\pi}{3} \right)} = 0
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
sin⁡(2x−π3)=0\sin{\left(2 x - \frac{\pi}{3} \right)} = 0
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
cos⁡(2x+π6)=0\cos{\left(2 x + \frac{\pi}{6} \right)} = 0
Esta ecuación se reorganiza en
2x+π6=πn+acos⁡(0)2 x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(0 \right)}
2x+π6=πn−π+acos⁡(0)2 x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}
O
2x+π6=πn+π22 x + \frac{\pi}{6} = \pi n + \frac{\pi}{2}
2x+π6=πn−π22 x + \frac{\pi}{6} = \pi n - \frac{\pi}{2}
, donde n es cualquier número entero
Transportemos
π6\frac{\pi}{6}
al miembro derecho de la ecuación
con el signo opuesto, en total:
2x=πn+π32 x = \pi n + \frac{\pi}{3}
2x=πn−2π32 x = \pi n - \frac{2 \pi}{3}
Dividamos ambos miembros de la ecuación obtenida en
22
obtenemos la respuesta:
x1=πn2+π6x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}
x2=πn2−π3x_{2} = \frac{\pi n}{2} - \frac{\pi}{3}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     pi
x1 = --
     6
x1=π6x_{1} = \frac{\pi}{6} 
     2*pi
x2 = ----
      3
x2=2π3x_{2} = \frac{2 \pi}{3} 
x2 = 2*pi/3
Suma y producto de raíces [src] 
suma
pi   2*pi
-- + ----
6     3
π6+2π3\frac{\pi}{6} + \frac{2 \pi}{3} 
=
5*pi
----
 6
5π6\frac{5 \pi}{6} 
producto
pi 2*pi
--*----
6   3
π62π3\frac{\pi}{6} \frac{2 \pi}{3} 
=
  2
pi 
---
 9
π29\frac{\pi^{2}}{9} 
pi^2/9
Respuesta numérica [src] 
x1 = 38.2227106186758
x2 = 88.4881930761125
x3 = 11.5191730631626
x4 = 97.9129710368819
x5 = -51.3126800086333
x6 = -56.025068989018
x7 = -26.1799387799149
x8 = 99.4837673636768
x9 = -35.6047167406843
x10 = -76.4454212373516
x11 = -73.3038285837618
x12 = 60.2138591938044
x13 = -13.6135681655558
x14 = 27.2271363311115
x15 = -7.33038285837618
x16 = 25.6563400043166
x17 = -84.2994028713261
x18 = 90.0589894029074
x19 = -100.007366139275
x20 = 68.0678408277789
x21 = 83.7758040957278
x22 = 8.37758040957278
x23 = 66.497044500984
x24 = -78.0162175641465
x25 = 36.6519142918809
x26 = 2.0943951023932
x27 = 55.5014702134197
x28 = -19.8967534727354
x29 = 69.6386371545737
x30 = 91.6297857297023
x31 = 53.9306738866248
x32 = -16.7551608191456
x33 = 17.8023583703422
x34 = 61.7846555205993
x35 = -12.0427718387609
x36 = 1228.88632632921
x37 = 82.2050077689329
x38 = -21.4675497995303
x39 = 14.6607657167524
x40 = 24.0855436775217
x41 = 9.94837673636768
x42 = 75.9218224617533
x43 = 52.3598775598299
x44 = -49.7418836818384
x45 = -54.4542726622231
x46 = 44.5058959258554
x47 = -93.7241808320955
x48 = 94.7713783832921
x49 = -43.4586983746588
x50 = -71.733032256967
x51 = 58.6430628670095
x52 = 3.66519142918809
x53 = -92.1533845053006
x54 = -87.4409955249159
x55 = -40.317105721069
x56 = 96.342174710087
x57 = -29.3215314335047
x58 = -57.5958653158129
x59 = -48.1710873550435
x60 = 0.523598775598299
x61 = 39.7935069454707
x62 = -32.4631240870945
x63 = -85.870199198121
x64 = 31.9395253114962
x65 = 47.6474885794452
x66 = -95.2949771588904
x67 = -5.75958653158129
x68 = -79.5870138909414
x69 = -27.7507351067098
x70 = 77.4926187885482
x71 = -34.0339204138894
x72 = -10.471975511966
x73 = -65.4498469497874
x74 = 80.634211442138
x75 = -62.3082542961976
x76 = -4.18879020478639
x77 = -18.3259571459405
x78 = 33.5103216382911
x79 = -41.8879020478639
x80 = 46.0766922526503
x81 = 22.5147473507269
x82 = -70.162235930172
x83 = 16.2315620435473
x84 = -98.4365698124802
x85 = 74.3510261349584
x86 = 30.3687289847013
x87 = -63.8790506229925
x87 = -63.8790506229925
Gráfico
sin(2*x-pi/3)=0 la ecuación
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