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-2sin(2x)+1=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
-2*sin(2*x) + 1 = 0
$$1 - 2 \sin{\left(2 x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$1 - 2 \sin{\left(2 x \right)} = 0$$
es la ecuación trigonométrica más simple
Transportemos 1 al miembro derecho de la ecuación

cambiando el signo de 1

Obtenemos:
$$- 2 \sin{\left(2 x \right)} = -1$$
Dividamos ambos miembros de la ecuación en -2

La ecuación se convierte en
$$\sin{\left(2 x \right)} = \frac{1}{2}$$
Esta ecuación se reorganiza en
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
O
$$2 x = 2 \pi n + \frac{\pi}{6}$$
$$2 x = 2 \pi n + \frac{5 \pi}{6}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \pi n + \frac{\pi}{12}$$
$$x_{2} = \pi n + \frac{5 \pi}{12}$$
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     12
$$x_{1} = \frac{\pi}{12}$$
     5*pi
x2 = ----
      12 
$$x_{2} = \frac{5 \pi}{12}$$
x2 = 5*pi/12
Respuesta numérica [src]
x1 = -87.7027949127151
x2 = 50.5272818452358
x3 = -71.9948316447661
x4 = -6.02138591938044
x5 = -80.3724120543389
x6 = -65.7116463375865
x7 = 31.6777259236971
x8 = 26.4417381677141
x9 = -36.3901149040818
x10 = -31.1541271480988
x11 = -17.540558982543
x12 = -64.6644487863899
x13 = 44.2440965380563
x14 = 12.8281700021583
x15 = -43.720497762458
x16 = 73.565627971561
x17 = -78.2780169519457
x18 = -34.2957198016886
x19 = -694.030177055545
x20 = -59.4284610304069
x21 = 88.2263936883134
x22 = 100.792764302673
x23 = -9.16297857297023
x24 = -28.012534494509
x25 = -100.269165527074
x26 = 35.8665161284835
x27 = 34.8193185772869
x28 = 0.261799387799149
x29 = 45.2912940892529
x30 = -30.1069295969022
x31 = -75.1364242983559
x32 = 56.8104671524154
x33 = -81.4196096055355
x34 = -93.9859802198946
x35 = 7.59218224617533
x36 = -14.3989663289532
x37 = 4.45058959258554
x38 = 13.8753675533549
x39 = -83.5140047079287
x40 = -58.3812634792103
x41 = 64.1408500107916
x42 = -12.30457122656
x43 = 42.1497014356631
x44 = 29.5833308213039
x45 = -61.5228561328001
x46 = -50.0036830696375
x47 = 92.4151838930998
x48 = -8.11578102177363
x49 = 86.1319985859202
x50 = 70.4240353179712
x51 = -74.0892267471593
x52 = 66.2352451131848
x53 = 94.5095789954929
x54 = 75.6600230739542
x55 = 57.857664703612
x56 = 22.2529479629277
x57 = -21.7293491873294
x58 = 79.8488132787406
x59 = -52.0980781720307
x60 = -39.5317075576716
x61 = 37.9609112308767
x62 = 59.9520598060052
x63 = -23.8237442897226
x64 = -86.6555973615185
x65 = -67.8060414399797
x66 = -37.4373124552784
x67 = 95.5567765466895
x68 = -42.6733002112614
x69 = 53.6688744988256
x70 = 20.1585528605345
x71 = -96.0803753222878
x72 = 72.5184304203644
x73 = 81.9432083811338
x74 = 48.4328867428426
x75 = -55.2396708256205
x76 = 78.801615727544
x77 = -89.7971900151083
x78 = -45.8148928648512
x79 = 28.5361332701073
x80 = -1.83259571459405
x81 = 15.9697626557481
x82 = -56.2868683768171
x83 = 6.54498469497874
x84 = -40.5789051088682
x85 = -53.1452757232273
x86 = 51.5744793964324
x87 = -97.1275728734844
x88 = 9.68657734856853
x89 = -15.4461638801498
x89 = -15.4461638801498