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ctg(x)=-√3

ctg(x)=-√3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
            ___
cot(x) = -\/ 3 
$$\cot{\left(x \right)} = - \sqrt{3}$$
Solución detallada
Tenemos la ecuación
$$\cot{\left(x \right)} = - \sqrt{3}$$
cambiamos
$$\cot{\left(x \right)} - 1 + \sqrt{3} = 0$$
$$\cot{\left(x \right)} - 1 + \sqrt{3} = 0$$
Sustituimos
$$w = \cot{\left(x \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 + w + sqrt3 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w + \sqrt{3} = 1$$
Dividamos ambos miembros de la ecuación en (w + sqrt(3))/w
w = 1 / ((w + sqrt(3))/w)

Obtenemos la respuesta: w = 1 - sqrt(3)
hacemos cambio inverso
$$\cot{\left(x \right)} = w$$
sustituimos w:
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 = -3.66519142918809
x2 = 90.5825881785057
x3 = 18.3259571459405
x4 = 93.7241808320955
x5 = -57.0722665402146
x6 = -25.6563400043166
x7 = 56.025068989018
x8 = 27.7507351067098
x9 = 5.75958653158129
x10 = 15.1843644923507
x11 = -82.2050077689329
x12 = 81.1578102177363
x13 = -28.7979326579064
x14 = -91.6297857297023
x15 = -72.7802298081635
x16 = -0.523598775598299
x17 = 68.5914396033772
x18 = 43.4586983746588
x19 = 96.8657734856853
x20 = 100.007366139275
x21 = -9.94837673636768
x22 = 34.0339204138894
x23 = 30.8923277602996
x24 = 65.4498469497874
x25 = -66.497044500984
x26 = 37.1755130674792
x27 = -16.2315620435473
x28 = -63.3554518473942
x29 = -44.5058959258554
x30 = 8.90117918517108
x31 = 52.8834763354282
x32 = -41.3643032722656
x33 = -31.9395253114962
x34 = 2.61799387799149
x35 = 21.4675497995303
x36 = -85.3466004225227
x37 = -97.9129710368819
x38 = -88.4881930761125
x39 = -69.6386371545737
x40 = -50.789081233035
x41 = 84.2994028713261
x42 = -6.80678408277789
x43 = -19.3731546971371
x44 = -53.9306738866248
x45 = 87.4409955249159
x46 = -22.5147473507269
x47 = -60.2138591938044
x48 = -38.2227106186758
x49 = 62.3082542961976
x50 = -94.7713783832921
x51 = 46.6002910282486
x52 = 40.317105721069
x53 = 74.8746249105567
x54 = 49.7418836818384
x55 = 12.0427718387609
x56 = 78.0162175641465
x57 = -47.6474885794452
x58 = 59.1666616426078
x59 = -13.0899693899575
x60 = 24.60914245312
x61 = 71.733032256967
x62 = -75.9218224617533
x63 = -79.0634151153431
x63 = -79.0634151153431
Gráfico
ctg(x)=-√3 la ecuación