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cos(2*x)=-1/2

cos(2*x)=-1/2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(2*x) = -1/2
$$\cos{\left(2 x \right)} = - \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(2 x \right)} = - \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
O
$$2 x = \pi n + \frac{2 \pi}{3}$$
$$2 x = \pi n - \frac{\pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{3}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{6}$$
Gráfica
Suma y producto de raíces [src]
suma
pi   2*pi
-- + ----
3     3  
$$\frac{\pi}{3} + \frac{2 \pi}{3}$$
=
pi
$$\pi$$
producto
pi 2*pi
--*----
3   3  
$$\frac{\pi}{3} \frac{2 \pi}{3}$$
=
    2
2*pi 
-----
  9  
$$\frac{2 \pi^{2}}{9}$$
2*pi^2/9
Respuesta rápida [src]
     pi
x1 = --
     3 
$$x_{1} = \frac{\pi}{3}$$
     2*pi
x2 = ----
      3  
$$x_{2} = \frac{2 \pi}{3}$$
x2 = 2*pi/3
Respuesta numérica [src]
x1 = 26.1799387799149
x2 = 11.5191730631626
x3 = -26.1799387799149
x4 = 99.4837673636768
x5 = -35.6047167406843
x6 = -76.4454212373516
x7 = 1515.29485658148
x8 = -13.6135681655558
x9 = -27.2271363311115
x10 = 92.1533845053006
x11 = 90.0589894029074
x12 = -14.6607657167524
x13 = -33.5103216382911
x14 = 4.18879020478639
x15 = 68.0678408277789
x16 = -77.4926187885482
x17 = -5.23598775598299
x18 = 83.7758040957278
x19 = 8.37758040957278
x20 = -378.038315981972
x21 = -99.4837673636768
x22 = -71.2094334813686
x23 = -93.2005820564972
x24 = 2.0943951023932
x25 = 55.5014702134197
x26 = -96.342174710087
x27 = -19.8967534727354
x28 = 54.4542726622231
x29 = -55.5014702134197
x30 = 17.8023583703422
x31 = 61.7846555205993
x32 = -68.0678408277789
x33 = 24.0855436775217
x34 = 30.3687289847013
x35 = 70.162235930172
x36 = 16.7551608191456
x37 = 48.1710873550435
x38 = -11.5191730631626
x39 = 52.3598775598299
x40 = -46.0766922526503
x41 = -54.4542726622231
x42 = 79.5870138909414
x43 = 82.7286065445312
x44 = 63.8790506229925
x45 = 76.4454212373516
x46 = -17.8023583703422
x47 = 41.8879020478639
x48 = 10.471975511966
x49 = -92.1533845053006
x50 = 96.342174710087
x51 = -57.5958653158129
x52 = -48.1710873550435
x53 = -2.0943951023932
x54 = 60.7374579694027
x55 = 98.4365698124802
x56 = -60.7374579694027
x57 = 85.870199198121
x58 = 39.7935069454707
x59 = -32.4631240870945
x60 = -85.870199198121
x61 = 19.8967534727354
x62 = -79.5870138909414
x63 = 32.4631240870945
x64 = -294.262511886244
x65 = -30.3687289847013
x66 = -49.2182849062401
x67 = 20.943951023932
x68 = 77.4926187885482
x69 = -10.471975511966
x70 = 33.5103216382911
x71 = -39.7935069454707
x72 = -4.18879020478639
x73 = -41.8879020478639
x74 = 46.0766922526503
x75 = -24.0855436775217
x76 = -70.162235930172
x77 = -98.4365698124802
x78 = 38.7463093942741
x79 = -90.0589894029074
x80 = 74.3510261349584
x81 = -83.7758040957278
x82 = -61.7846555205993
x83 = -63.8790506229925
x83 = -63.8790506229925
Gráfico
cos(2*x)=-1/2 la ecuación