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-cos(x)=-(√3/2) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
             ___ 
          -\/ 3  
-cos(x) = -------
             2   
$$- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
Solución detallada
Tenemos la ecuación
$$- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
O
$$x = \pi n + \frac{\pi}{6}$$
$$x = \pi n - \frac{5 \pi}{6}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     6 
$$x_{1} = \frac{\pi}{6}$$
     11*pi
x2 = -----
       6  
$$x_{2} = \frac{11 \pi}{6}$$
x2 = 11*pi/6
Suma y producto de raíces [src]
suma
pi   11*pi
-- + -----
6      6  
$$\frac{\pi}{6} + \frac{11 \pi}{6}$$
=
2*pi
$$2 \pi$$
producto
pi 11*pi
--*-----
6    6  
$$\frac{\pi}{6} \frac{11 \pi}{6}$$
=
     2
11*pi 
------
  36  
$$\frac{11 \pi^{2}}{36}$$
11*pi^2/36
Respuesta numérica [src]
x1 = -18.3259571459405
x2 = -12.0427718387609
x3 = -75.9218224617533
x4 = 30.8923277602996
x5 = -6.80678408277789
x6 = -49.7418836818384
x7 = 43.4586983746588
x8 = 93.7241808320955
x9 = 44.5058959258554
x10 = -81.1578102177363
x11 = -74.8746249105567
x12 = -24.60914245312
x13 = 19.3731546971371
x14 = -50.789081233035
x15 = -19.3731546971371
x16 = -31.9395253114962
x17 = 24.60914245312
x18 = 37.1755130674792
x19 = 31.9395253114962
x20 = -100.007366139275
x21 = 63.3554518473942
x22 = -0.523598775598299
x23 = 57.0722665402146
x24 = -82.2050077689329
x25 = 12.0427718387609
x26 = 74.8746249105567
x27 = -68.5914396033772
x28 = -30.8923277602996
x29 = -93.7241808320955
x30 = 69.6386371545737
x31 = 38.2227106186758
x32 = -57.0722665402146
x33 = -37.1755130674792
x34 = 194.255145746969
x35 = -69.6386371545737
x36 = 0.523598775598299
x37 = -43.4586983746588
x38 = 87.4409955249159
x39 = 13.0899693899575
x40 = -5.75958653158129
x41 = -38.2227106186758
x42 = 6.80678408277789
x43 = -101.054563690472
x44 = 62.3082542961976
x45 = 100.007366139275
x46 = -13.0899693899575
x47 = 5.75958653158129
x48 = 49.7418836818384
x49 = -56.025068989018
x50 = -62.3082542961976
x51 = 82.2050077689329
x52 = 94.7713783832921
x53 = 1168.1488683598
x54 = -87.4409955249159
x55 = 68.5914396033772
x56 = -88.4881930761125
x57 = 88.4881930761125
x58 = -25.6563400043166
x59 = -63.3554518473942
x60 = -94.7713783832921
x61 = 56.025068989018
x62 = -44.5058959258554
x63 = 50.789081233035
x64 = 25.6563400043166
x65 = 18.3259571459405
x66 = 81.1578102177363
x67 = 75.9218224617533
x67 = 75.9218224617533