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cos((𝜋/3)−𝑥)+1/2=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   /pi    \   1    
cos|-- - x| + - = 0
   \3     /   2
cos⁡(−x+π3)+12=0\cos{\left(- x + \frac{\pi}{3} \right)} + \frac{1}{2} = 0
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(−x+π3)+12=0\cos{\left(- x + \frac{\pi}{3} \right)} + \frac{1}{2} = 0
es la ecuación trigonométrica más simple
Transportemos 1/2 al miembro derecho de la ecuación

cambiando el signo de 1/2

Obtenemos:
cos⁡(−x+π3)=−12\cos{\left(- x + \frac{\pi}{3} \right)} = - \frac{1}{2}
Esta ecuación se reorganiza en
x+π6=2πn+asin⁡(−12)x + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}
x+π6=2πn−asin⁡(−12)+πx + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi
O
x+π6=2πn−π6x + \frac{\pi}{6} = 2 \pi n - \frac{\pi}{6}
x+π6=2πn+7π6x + \frac{\pi}{6} = 2 \pi n + \frac{7 \pi}{6}
, donde n es cualquier número entero
Transportemos
π6\frac{\pi}{6}
al miembro derecho de la ecuación
con el signo opuesto, en total:
x=2πn−π3x = 2 \pi n - \frac{\pi}{3}
x=2πn+πx = 2 \pi n + \pi
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
  pi     
- -- + pi
  3
π−π3\pi - \frac{\pi}{3} 
=
2*pi
----
 3
2π3\frac{2 \pi}{3} 
producto
-pi    
----*pi
 3
−π3π- \frac{\pi}{3} \pi 
=
   2 
-pi  
-----
  3
−π23- \frac{\pi^{2}}{3} 
-pi^2/3
Respuesta rápida [src] 
     -pi 
x1 = ----
      3
x1=−π3x_{1} = - \frac{\pi}{3} 
x2 = pi
x2=πx_{2} = \pi 
x2 = pi
Respuesta numérica [src] 
x1 = 72.2566310325652
x2 = -103.672557568463
x3 = -59.6902604182061
x4 = 3.14159265358979
x5 = -51.3126800086333
x6 = 99.4837673636768
x7 = 28.2743338823081
x8 = 80.634211442138
x9 = 93.2005820564972
x10 = -9.42477796076938
x11 = 65.9734457253857
x12 = 40.8407044966673
x13 = -57.5958653158129
x14 = -38.7463093942741
x15 = 49.2182849062401
x16 = -32.4631240870945
x17 = -3.14159265358979
x18 = -15.707963267949
x19 = 59.6902604182061
x20 = 24.0855436775217
x21 = 55.5014702134197
x22 = 9.42477796076938
x23 = 11.5191730631626
x24 = -53.4070751110265
x25 = -47.1238898038469
x26 = -84.8230016469244
x27 = 21.9911485751286
x28 = -72.2566310325652
x29 = -63.8790506229925
x30 = 34.5575191894877
x31 = -21.9911485751286
x32 = -65.9734457253857
x33 = -13.6135681655558
x34 = -89.0117918517108
x35 = 86.9173967493176
x36 = 30.3687289847013
x37 = 53.4070751110265
x38 = -95.2949771588904
x39 = -28.2743338823081
x40 = 15.707963267949
x41 = -45.0294947014537
x42 = -91.106186954104
x43 = 47.1238898038469
x44 = 97.3893722612836
x45 = -19.8967534727354
x46 = -82.7286065445312
x47 = -1.0471975511966
x48 = 61.7846555205993
x49 = -76.4454212373516
x50 = 78.5398163397448
x51 = 42.9350995990605
x52 = -78.5398163397448
x53 = 17.8023583703422
x54 = -40.8407044966673
x55 = -97.3893722612836
x56 = -70.162235930172
x57 = -220.958683302482
x58 = 84.8230016469244
x59 = 91.106186954104
x60 = -26.1799387799149
x61 = 36.6519142918809
x62 = 68.0678408277789
x63 = 74.3510261349584
x64 = -7.33038285837618
x65 = -34.5575191894877
x66 = 5.23598775598299
x66 = 5.23598775598299
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