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cos*((pi*(x-7))/3)=1/2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /pi*(x - 7)\      
cos|----------| = 1/2
   \    3     /      
$$\cos{\left(\frac{\pi \left(x - 7\right)}{3} \right)} = \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(\frac{\pi \left(x - 7\right)}{3} \right)} = \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
O
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \frac{5 \pi}{6}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{6}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$\frac{\pi x}{3} = 2 \pi n$$
$$\frac{\pi x}{3} = 2 \pi n + \frac{2 \pi}{3}$$
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{\pi}{3}$$
obtenemos la respuesta:
$$x_{1} = 6 n$$
$$x_{2} = \frac{3 \left(2 \pi n + \frac{2 \pi}{3}\right)}{\pi}$$
Gráfica
Suma y producto de raíces [src]
suma
2
$$2$$
=
2
$$2$$
producto
0*2
$$0 \cdot 2$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
x2 = 2
$$x_{2} = 2$$
x2 = 2
Respuesta numérica [src]
x1 = 38.0
x2 = -6.0
x3 = 26.0
x4 = -64.0
x5 = -58.0
x6 = -70.0
x7 = 48.0
x8 = 446.0
x9 = -46.0
x10 = 78.0
x11 = -10.0
x12 = 30.0
x13 = 488.0
x14 = 60.0
x15 = -93744.0
x16 = 90.0
x17 = 18.0
x18 = 50.0
x19 = 92.0
x20 = 644.0
x21 = 36.0
x22 = -30.0
x23 = 20.0
x24 = 84.0
x25 = -18.0
x26 = -100.0
x27 = -42.0
x28 = -90.0
x29 = -78.0
x30 = 44.0
x31 = 98.0
x32 = 80.0
x33 = -72.0
x34 = 74.0
x35 = 8.0
x36 = -876.0
x37 = -96.0
x38 = -66.0
x39 = 96.0
x40 = -76.0
x41 = 66.0
x42 = -28.0
x43 = 24.0
x44 = -84.0
x45 = 32.0
x46 = 14.0
x47 = 6.0
x48 = -60.0
x49 = 752.0
x50 = 2.0
x51 = -36.0
x52 = -12.0
x53 = 56.0
x54 = -16.0
x55 = -34.0
x56 = -52.0
x57 = 62.0
x58 = -88.0
x59 = -94.0
x60 = -24.0
x61 = 42.0
x62 = -22.0
x63 = -82.0
x64 = 68.0
x65 = 600.0
x66 = -4.0
x67 = 86.0
x68 = 54.0
x69 = -48.0
x70 = -54.0
x71 = 72.0
x72 = -40.0
x73 = 12.0
x73 = 12.0