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sin2x=-1/2

sin2x=-1/2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sin(2*x) = -1/2
$$\sin{\left(2 x \right)} = - \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(2 x \right)} = - \frac{1}{2}$$
es la ecuación trigonométrica más simple
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
$$2 x = 2 \pi n - \frac{\pi}{6}$$
$$2 x = 2 \pi n + \frac{7 \pi}{6}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \pi n - \frac{\pi}{12}$$
$$x_{2} = \pi n + \frac{7 \pi}{12}$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   7*pi
- -- + ----
  12    12 
$$- \frac{\pi}{12} + \frac{7 \pi}{12}$$
=
pi
--
2 
$$\frac{\pi}{2}$$
producto
-pi  7*pi
----*----
 12   12 
$$- \frac{\pi}{12} \frac{7 \pi}{12}$$
=
     2
-7*pi 
------
 144  
$$- \frac{7 \pi^{2}}{144}$$
-7*pi^2/144
Respuesta rápida [src]
     -pi 
x1 = ----
      12 
$$x_{1} = - \frac{\pi}{12}$$
     7*pi
x2 = ----
      12 
$$x_{2} = \frac{7 \pi}{12}$$
x2 = 7*pi/12
Respuesta numérica [src]
x1 = 42.6733002112614
x2 = 84.5612022591253
x3 = -89.27359123951
x4 = 127.496301858186
x5 = 30.1069295969022
x6 = 8.11578102177363
x7 = 28.012534494509
x8 = 6.02138591938044
x9 = 36.3901149040818
x10 = -28.5361332701073
x11 = -88.2263936883134
x12 = 14.3989663289532
x13 = -51.5744793964324
x14 = 100.269165527074
x15 = 50.0036830696375
x16 = -15.9697626557481
x17 = -66.2352451131848
x18 = 23.8237442897226
x19 = -35.8665161284835
x20 = -31.6777259236971
x21 = 20.6821516361328
x22 = 67.8060414399797
x23 = -17.0169602069447
x24 = -53.6688744988256
x25 = 43.720497762458
x26 = -91.3679863419031
x27 = 59.4284610304069
x28 = 74.0892267471593
x29 = -0.261799387799149
x30 = -45.2912940892529
x31 = 40.5789051088682
x32 = -72.5184304203644
x33 = 78.2780169519457
x34 = 93.9859802198946
x35 = 86.6555973615185
x36 = -23.3001455141243
x37 = 21.7293491873294
x38 = -44.2440965380563
x39 = -64.1408500107916
x40 = -95.5567765466895
x41 = -29.5833308213039
x42 = 1.83259571459405
x43 = 87.7027949127151
x44 = -42.1497014356631
x45 = -20.1585528605345
x46 = -57.857664703612
x47 = -79.8488132787406
x48 = 56.2868683768171
x49 = -86.1319985859202
x50 = -50.5272818452358
x51 = 45.8148928648512
x52 = 64.6644487863899
x53 = -75.6600230739542
x54 = -13.8753675533549
x55 = 62.5700536839967
x56 = -81.9432083811338
x57 = 65.7116463375865
x58 = -7.59218224617533
x59 = -6.54498469497874
x60 = -73.565627971561
x61 = 89.7971900151083
x62 = 12.30457122656
x63 = 58.3812634792103
x64 = -67.2824426643814
x65 = -37.9609112308767
x66 = -22.2529479629277
x67 = 90.8443875663049
x68 = 96.0803753222878
x69 = -94.5095789954929
x70 = 81.4196096055355
x71 = -1926.05809603834
x72 = 80.3724120543389
x73 = 52.0980781720307
x74 = 37.4373124552784
x75 = 71.9948316447661
x76 = -1.30899693899575
x77 = -97.6511716490827
x78 = 15.4461638801498
x79 = -9.68657734856853
x80 = 34.2957198016886
x81 = -59.9520598060052
x82 = 18.5877565337396
x82 = 18.5877565337396
Gráfico
sin2x=-1/2 la ecuación