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sqrt3*sin(x)+cos(x)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
  ___                    
\/ 3 *sin(x) + cos(x) = 0
$$\sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
cambiamos:
$$\frac{\sqrt{3} \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
o
$$\sqrt{3} \tan{\left(x \right)} = -1$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en sqrt(3)

La ecuación se convierte en
$$\tan{\left(x \right)} = \frac{\sqrt{3}}{3}$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
O
$$x = \pi n + \frac{\pi}{6}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
-pi 
----
 6  
$$- \frac{\pi}{6}$$
=
-pi 
----
 6  
$$- \frac{\pi}{6}$$
producto
-pi 
----
 6  
$$- \frac{\pi}{6}$$
=
-pi 
----
 6  
$$- \frac{\pi}{6}$$
-pi/6
Respuesta rápida [src]
     -pi 
x1 = ----
      6  
$$x_{1} = - \frac{\pi}{6}$$
x1 = -pi/6
Respuesta numérica [src]
x1 = 8.90117918517108
x2 = 90.5825881785057
x3 = 71.733032256967
x4 = -75.9218224617533
x5 = -60.2138591938044
x6 = -914.727060970228
x7 = 30.8923277602996
x8 = -6.80678408277789
x9 = 43.4586983746588
x10 = 93.7241808320955
x11 = -50.789081233035
x12 = -72.7802298081635
x13 = -19.3731546971371
x14 = -31.9395253114962
x15 = 37.1755130674792
x16 = 24.60914245312
x17 = -91.6297857297023
x18 = -9.94837673636768
x19 = -97.9129710368819
x20 = -82.2050077689329
x21 = 12.0427718387609
x22 = 78.0162175641465
x23 = -16.2315620435473
x24 = 74.8746249105567
x25 = 84.2994028713261
x26 = -22.5147473507269
x27 = 15.1843644923507
x28 = 46.6002910282486
x29 = -35.081117965086
x30 = 40.317105721069
x31 = 131.423292675173
x32 = 34.0339204138894
x33 = -3.66519142918809
x34 = -69.6386371545737
x35 = -47.6474885794452
x36 = 59.1666616426078
x37 = -66.497044500984
x38 = 2.61799387799149
x39 = -38.2227106186758
x40 = 65.4498469497874
x41 = -41.3643032722656
x42 = -101.054563690472
x43 = 87.4409955249159
x44 = 62.3082542961976
x45 = 100.007366139275
x46 = -13.0899693899575
x47 = 5.75958653158129
x48 = 52.8834763354282
x49 = 49.7418836818384
x50 = -28.7979326579064
x51 = 68.5914396033772
x52 = -88.4881930761125
x53 = -25.6563400043166
x54 = 96.8657734856853
x55 = -63.3554518473942
x56 = -94.7713783832921
x57 = 56.025068989018
x58 = -44.5058959258554
x59 = -79.0634151153431
x60 = -85.3466004225227
x61 = 21.4675497995303
x62 = -0.523598775598299
x63 = 27.7507351067098
x64 = 18.3259571459405
x65 = 81.1578102177363
x66 = -57.0722665402146
x67 = -53.9306738866248
x67 = -53.9306738866248