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1-2cosx=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
1 - 2*cos(x) = 0
$$1 - 2 \cos{\left(x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$1 - 2 \cos{\left(x \right)} = 0$$
es la ecuación trigonométrica más simple
Transportemos 1 al miembro derecho de la ecuación

cambiando el signo de 1

Obtenemos:
$$- 2 \cos{\left(x \right)} = -1$$
Dividamos ambos miembros de la ecuación en -2

La ecuación se convierte en
$$\cos{\left(x \right)} = \frac{1}{2}$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
pi   5*pi
-- + ----
3     3  
$$\frac{\pi}{3} + \frac{5 \pi}{3}$$
=
2*pi
$$2 \pi$$
producto
pi 5*pi
--*----
3   3  
$$\frac{\pi}{3} \frac{5 \pi}{3}$$
=
    2
5*pi 
-----
  9  
$$\frac{5 \pi^{2}}{9}$$
5*pi^2/9
Respuesta rápida [src]
     pi
x1 = --
     3 
$$x_{1} = \frac{\pi}{3}$$
     5*pi
x2 = ----
      3  
$$x_{2} = \frac{5 \pi}{3}$$
x2 = 5*pi/3
Respuesta numérica [src]
x1 = -82.7286065445312
x2 = -89.0117918517108
x3 = 45.0294947014537
x4 = -13.6135681655558
x5 = -17.8023583703422
x6 = 36.6519142918809
x7 = -80.634211442138
x8 = 86.9173967493176
x9 = -99.4837673636768
x10 = 30.3687289847013
x11 = 68.0678408277789
x12 = 61.7846555205993
x13 = -93.2005820564972
x14 = 26.1799387799149
x15 = 17.8023583703422
x16 = 89.0117918517108
x17 = 82.7286065445312
x18 = -55.5014702134197
x19 = -57.5958653158129
x20 = -63.8790506229925
x21 = -36.6519142918809
x22 = 76.4454212373516
x23 = 24.0855436775217
x24 = -76.4454212373516
x25 = -7.33038285837618
x26 = -45.0294947014537
x27 = -5.23598775598299
x28 = 57.5958653158129
x29 = -11.5191730631626
x30 = 7.33038285837618
x31 = -70.162235930172
x32 = -51.3126800086333
x33 = 55.5014702134197
x34 = 32.4631240870945
x35 = 99.4837673636768
x36 = 13.6135681655558
x37 = -225.147473507269
x38 = -24.0855436775217
x39 = -1.0471975511966
x40 = 63.8790506229925
x41 = -32.4631240870945
x42 = -30.3687289847013
x43 = 19.8967534727354
x44 = -68.0678408277789
x45 = 95.2949771588904
x46 = -359.188760060433
x47 = 49.2182849062401
x48 = 42.9350995990605
x49 = -49.2182849062401
x50 = 74.3510261349584
x51 = 1651.43053823704
x52 = 11.5191730631626
x53 = -95.2949771588904
x54 = 51.3126800086333
x55 = -26.1799387799149
x56 = 93.2005820564972
x57 = -38.7463093942741
x58 = -61.7846555205993
x59 = 80.634211442138
x60 = 70.162235930172
x61 = 1.0471975511966
x62 = -19.8967534727354
x63 = -74.3510261349584
x64 = 38.7463093942741
x65 = -86.9173967493176
x66 = 5.23598775598299
x67 = -42.9350995990605
x67 = -42.9350995990605