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cos(x+pi/3)=(-1)/sqrt(2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /    pi\    -1  
cos|x + --| = -----
   \    3 /     ___
              \/ 2
cos⁡(x+π3)=−12\cos{\left(x + \frac{\pi}{3} \right)} = - \frac{1}{\sqrt{2}}
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(x+π3)=−12\cos{\left(x + \frac{\pi}{3} \right)} = - \frac{1}{\sqrt{2}}
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x+π3=πn+acos⁡(−22)x + \frac{\pi}{3} = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}
x+π3=πn−π+acos⁡(−22)x + \frac{\pi}{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}
O
x+π3=πn+3π4x + \frac{\pi}{3} = \pi n + \frac{3 \pi}{4}
x+π3=πn−π4x + \frac{\pi}{3} = \pi n - \frac{\pi}{4}
, donde n es cualquier número entero
Transportemos
π3\frac{\pi}{3}
al miembro derecho de la ecuación
con el signo opuesto, en total:
x=πn+5π12x = \pi n + \frac{5 \pi}{12}
x=πn−7π12x = \pi n - \frac{7 \pi}{12}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     5*pi
x1 = ----
      12
x1=5π12x_{1} = \frac{5 \pi}{12} 
     11*pi
x2 = -----
       12
x2=11π12x_{2} = \frac{11 \pi}{12} 
x2 = 11*pi/12
Suma y producto de raíces [src] 
suma
5*pi   11*pi
---- + -----
 12      12
5π12+11π12\frac{5 \pi}{12} + \frac{11 \pi}{12} 
=
4*pi
----
 3
4π3\frac{4 \pi}{3} 
producto
5*pi 11*pi
----*-----
 12    12
5π1211π12\frac{5 \pi}{12} \frac{11 \pi}{12} 
=
     2
55*pi 
------
 144
55π2144\frac{55 \pi^{2}}{144} 
55*pi^2/144
Respuesta numérica [src] 
x1 = 57.857664703612
x2 = 90.8443875663049
x3 = 95.5567765466895
x4 = 158.388629618485
x5 = -48.9564855184409
x6 = -41.1025038844665
x7 = 46.8620904160477
x8 = 40.5789051088682
x9 = 725.446103591443
x10 = 20.1585528605345
x11 = -53.6688744988256
x12 = 1.30899693899575
x13 = -55.2396708256205
x14 = -67.8060414399797
x15 = 84.5612022591253
x16 = -30.1069295969022
x17 = 13.8753675533549
x18 = 7.59218224617533
x19 = 89.27359123951
x20 = -3.40339204138894
x21 = -78.801615727544
x22 = 97.1275728734844
x23 = -61.5228561328001
x24 = -47.3856891916461
x25 = -34.8193185772869
x26 = 78.2780169519457
x27 = -91.3679863419031
x28 = -86.6555973615185
x29 = -59.9520598060052
x30 = -42.6733002112614
x31 = -36.3901149040818
x32 = 9.16297857297023
x33 = 65.7116463375865
x34 = -66.2352451131848
x35 = -22.2529479629277
x36 = -85.0848010347236
x37 = 2.87979326579064
x38 = -9.68657734856853
x39 = 45.2912940892529
x40 = -15.9697626557481
x41 = -92.9387826686981
x42 = 53.1452757232273
x43 = -4.97418836818384
x44 = -72.5184304203644
x45 = 32.7249234748937
x46 = -97.6511716490827
x47 = 59.4284610304069
x48 = 82.9904059323304
x49 = 76.7072206251508
x50 = -23.8237442897226
x51 = -80.3724120543389
x52 = 39.0081087820733
x53 = -17.540558982543
x54 = -11.2573736753634
x55 = 28.012534494509
x56 = -99.2219679758776
x57 = 70.4240353179712
x58 = 71.9948316447661
x59 = 51.5744793964324
x60 = -1871.08022460052
x61 = 21.7293491873294
x62 = -74.0892267471593
x63 = 951.640774649908
x64 = 64.1408500107916
x65 = 26.4417381677141
x66 = -28.5361332701073
x67 = 34.2957198016886
x68 = 101.839961853869
x69 = 415.999227212848
x70 = 15.4461638801498
x70 = 15.4461638801498
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