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sin(-x)=1/2

sin(-x)=1/2 la ecuación

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Solución numérica:

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Solución

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

La ecuación se convierte en
$$\sin{\left(x \right)} = - \frac{1}{2}$$
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
O
$$x = 2 \pi n - \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{7 \pi}{6}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      6  
$$x_{1} = - \frac{\pi}{6}$$
     7*pi
x2 = ----
      6  
$$x_{2} = \frac{7 \pi}{6}$$
x2 = 7*pi/6
Suma y producto de raíces [src]
suma
  pi   7*pi
- -- + ----
  6     6  
$$- \frac{\pi}{6} + \frac{7 \pi}{6}$$
=
pi
$$\pi$$
producto
-pi  7*pi
----*----
 6    6  
$$- \frac{\pi}{6} \frac{7 \pi}{6}$$
=
     2
-7*pi 
------
  36  
$$- \frac{7 \pi^{2}}{36}$$
-7*pi^2/36
Respuesta numérica [src]
x1 = -8.90117918517108
x2 = 66400.1787274983
x3 = -15.1843644923507
x4 = 18.3259571459405
x5 = 66.497044500984
x6 = 93.7241808320955
x7 = -57.0722665402146
x8 = 192.160750644576
x9 = -25.6563400043166
x10 = 56.025068989018
x11 = 47.6474885794452
x12 = -101.054563690472
x13 = -78.0162175641465
x14 = -52.8834763354282
x15 = 5.75958653158129
x16 = -82.2050077689329
x17 = 28.7979326579064
x18 = 81.1578102177363
x19 = 97.9129710368819
x20 = -0.523598775598299
x21 = 68.5914396033772
x22 = -90.5825881785057
x23 = 43.4586983746588
x24 = 100.007366139275
x25 = -46.6002910282486
x26 = 30.8923277602996
x27 = 37.1755130674792
x28 = -195.302343298165
x29 = -63.3554518473942
x30 = -27.7507351067098
x31 = -34.0339204138894
x32 = -44.5058959258554
x33 = -151.320046147908
x34 = 79.0634151153431
x35 = 91.6297857297023
x36 = -65.4498469497874
x37 = 72.7802298081635
x38 = 60.2138591938044
x39 = -71.733032256967
x40 = -31.9395253114962
x41 = 53.9306738866248
x42 = 3.66519142918809
x43 = 22.5147473507269
x44 = -84.2994028713261
x45 = 437.20497762458
x46 = -88.4881930761125
x47 = -40.317105721069
x48 = -69.6386371545737
x49 = -50.789081233035
x50 = -6.80678408277789
x51 = -19.3731546971371
x52 = 87.4409955249159
x53 = 16.2315620435473
x54 = -38.2227106186758
x55 = 62.3082542961976
x56 = -94.7713783832921
x57 = 49.7418836818384
x58 = -96.8657734856853
x59 = 74.8746249105567
x60 = 85.3466004225227
x61 = 12.0427718387609
x62 = -21.4675497995303
x63 = -59.1666616426078
x64 = -13.0899693899575
x65 = 41.3643032722656
x66 = 24.60914245312
x67 = 35.081117965086
x68 = -75.9218224617533
x69 = 9.94837673636768
x70 = -2.61799387799149
x70 = -2.61799387799149
Gráfico
sin(-x)=1/2 la ecuación