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cos(pi*x/3)=-1

cos(pi*x/3)=-1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   /pi*x\     
cos|----| = -1
   \ 3  /
cos⁡(πx3)=−1\cos{\left(\frac{\pi x}{3} \right)} = -1
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(πx3)=−1\cos{\left(\frac{\pi x}{3} \right)} = -1
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
πx3=πn+acos⁡(−1)\frac{\pi x}{3} = \pi n + \operatorname{acos}{\left(-1 \right)}
πx3=πn−π+acos⁡(−1)\frac{\pi x}{3} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}
O
πx3=πn+π\frac{\pi x}{3} = \pi n + \pi
πx3=πn\frac{\pi x}{3} = \pi n
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
π3\frac{\pi}{3}
obtenemos la respuesta:
x1=3(πn+π)πx_{1} = \frac{3 \left(\pi n + \pi\right)}{\pi}
x2=3nx_{2} = 3 n
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
3
33 
=
3
33 
producto
3
33 
=
3
33 
3
Respuesta rápida [src] 
x1 = 3
x1=3x_{1} = 3 
x1 = 3
Respuesta numérica [src] 
x1 = -81.0000003480541
x2 = 56.9999996519459
x3 = 33.0000002714011
x4 = -26.9999997285989
x5 = 57.0000004397617
x6 = 2.99999965194586
x7 = 69.0000002714011
x8 = -38.9999995602383
x9 = 62.9999996519459
x10 = -80.9999995602383
x11 = -68.9999997285989
x12 = -75.0000003480541
x13 = -45.0000003480541
x14 = -56.9999995602383
x15 = 63.0000002714011
x16 = 8.99999965194586
x17 = 44.9999996519459
x18 = 87.0000004397617
x19 = -80.9999997285989
x20 = -21.0000003480541
x21 = -56.9999997285989
x22 = 111.000000271401
x23 = 80.9999996519459
x24 = -14.9999995602383
x25 = 68.9999996519459
x26 = -74.9999997285989
x27 = -9.00000034805414
x28 = 69.0000004397617
x29 = -3.00000034805414
x30 = 51.0000004397617
x31 = -8.99999956023833
x32 = 3.00000043976167
x33 = -26.9999995602383
x34 = 9.00000043976167
x35 = 99.0000004397617
x36 = -8.99999972859885
x37 = 105.000000271401
x38 = 27.0000002714011
x39 = -32.9999995602383
x40 = -44.9999995602383
x41 = -98.9999995602383
x42 = -50.9999997285989
x43 = -57.0000003480541
x44 = 81.0000002714011
x45 = 87.0000002714011
x46 = -86.9999995602383
x47 = -14.9999997285989
x48 = 32.9999996519459
x49 = -87.0000003480541
x50 = 45.0000004397617
x51 = 39.0000002714011
x52 = -2.99999972859885
x53 = 93.0000004397617
x54 = -39.0000003480541
x55 = 50.9999996519459
x56 = 15.0000004397617
x57 = 38.9999996519459
x58 = -99.0000003480541
x59 = 57.0000002714011
x60 = -74.9999995602383
x61 = 14.9999996519459
x62 = 63.0000004397617
x63 = -62.9999997285989
x64 = -27.0000003480541
x65 = 9.00000027140115
x66 = -62.9999995602383
x67 = 33.0000004397617
x68 = -69.0000003480541
x69 = 74.9999996519459
x70 = -50.9999995602383
x71 = 15.0000002714011
x72 = -20.9999997285989
x73 = -51.0000003480541
x74 = 99.0000002714011
x75 = 21.0000004397617
x76 = 98.9999996519459
x77 = 21.0000002714011
x78 = -38.9999997285989
x79 = 93.0000002714011
x80 = 39.0000004397617
x81 = 45.0000002714011
x82 = 27.0000004397617
x83 = -32.9999997285989
x84 = 92.9999996519459
x85 = -68.9999995602383
x86 = -33.0000003480541
x87 = -20.9999995602383
x88 = 26.9999996519459
x89 = 81.0000004397617
x90 = 3.00000027140115
x91 = 75.0000004397617
x92 = -92.9999995602383
x93 = 51.0000002714011
x94 = 86.9999996519459
x95 = -44.9999997285989
x96 = 75.0000002714011
x97 = -2.99999956023833
x98 = -15.0000003480541
x99 = -93.0000003480541
x100 = 20.9999996519459
x101 = -63.0000003480541
x101 = -63.0000003480541
Gráfico
cos(pi*x/3)=-1 la ecuación
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