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cos(pi*x/3)=-1/2

cos(pi*x/3)=-1/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   /pi*x\       
cos|----| = -1/2
   \ 3  /       
$$\cos{\left(\frac{\pi x}{3} \right)} = - \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(\frac{\pi x}{3} \right)} = - \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{\pi x}{3} = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$\frac{\pi x}{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
O
$$\frac{\pi x}{3} = \pi n + \frac{2 \pi}{3}$$
$$\frac{\pi x}{3} = \pi n - \frac{\pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{\pi}{3}$$
obtenemos la respuesta:
$$x_{1} = \frac{3 \left(\pi n + \frac{2 \pi}{3}\right)}{\pi}$$
$$x_{2} = \frac{3 \left(\pi n - \frac{\pi}{3}\right)}{\pi}$$
Gráfica
Suma y producto de raíces [src]
suma
2 + 4
$$2 + 4$$
=
6
$$6$$
producto
2*4
$$2 \cdot 4$$
=
8
$$8$$
8
Respuesta rápida [src]
x1 = 2
$$x_{1} = 2$$
x2 = 4
$$x_{2} = 4$$
x2 = 4
Respuesta numérica [src]
x1 = 16.0
x2 = 10.0
x3 = 626.0
x4 = -82.0
x5 = 490.0
x6 = -62.0
x7 = -98.0
x8 = 26.0
x9 = 86.0
x10 = 50.0
x11 = -46.0
x12 = 100.0
x13 = 28.0
x14 = -8.0
x15 = 88.0
x16 = -76.0
x17 = -100.0
x18 = -26.0
x19 = 484.0
x20 = -4.0
x21 = -44.0
x22 = 574.0
x23 = 94.0
x24 = 20.0
x25 = 64.0
x26 = -20.0
x27 = 584.0
x28 = -2.0
x29 = -38.0
x30 = 58.0
x31 = -68.0
x32 = 82.0
x33 = 560.0
x34 = -58.0
x35 = 616.0
x36 = 44.0
x37 = 14.0
x38 = -70.0
x39 = 52.0
x40 = -88.0
x41 = -22.0
x42 = 76.0
x43 = 40.0
x44 = -94.0
x45 = 74.0
x46 = -10.0
x47 = -92.0
x48 = -52.0
x49 = -40.0
x50 = 536.0
x51 = 70.0
x52 = -16.0
x53 = -80.0
x54 = 62.0
x55 = -86.0
x56 = -74.0
x57 = -28.0
x58 = -34.0
x59 = -56.0
x60 = -14.0
x61 = 2.0
x62 = -64.0
x63 = -9686.0
x64 = -32.0
x65 = 98.0
x66 = 56.0
x67 = 46.0
x68 = 568.0
x69 = 34.0
x70 = 68.0
x71 = 92.0
x72 = 80.0
x73 = 8.0
x74 = 38.0
x75 = 22.0
x76 = 4.0
x77 = 32.0
x78 = -50.0
x78 = -50.0
Gráfico
cos(pi*x/3)=-1/2 la ecuación