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cos(2*x)=0,1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(2*x) = 1/10
cos⁡(2x)=110\cos{\left(2 x \right)} = \frac{1}{10}
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(2x)=110\cos{\left(2 x \right)} = \frac{1}{10}
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
2x=πn+acos⁡(110)2 x = \pi n + \operatorname{acos}{\left(\frac{1}{10} \right)}
2x=πn−π+acos⁡(110)2 x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{10} \right)}
O
2x=πn+acos⁡(110)2 x = \pi n + \operatorname{acos}{\left(\frac{1}{10} \right)}
2x=πn−π+acos⁡(110)2 x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{10} \right)}
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
22
obtenemos la respuesta:
x1=πn2+acos⁡(110)2x_{1} = \frac{\pi n}{2} + \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2}
x2=πn2−π2+acos⁡(110)2x_{2} = \frac{\pi n}{2} - \frac{\pi}{2} + \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
          acos(1/10)
x1 = pi - ----------
              2
x1=π−acos⁡(110)2x_{1} = \pi - \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2} 
     acos(1/10)
x2 = ----------
         2
x2=acos⁡(110)2x_{2} = \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2} 
x2 = acos(1/10)/2
Suma y producto de raíces [src] 
suma
     acos(1/10)   acos(1/10)
pi - ---------- + ----------
         2            2
acos⁡(110)2+(π−acos⁡(110)2)\frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2} + \left(\pi - \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2}\right) 
=
pi
π\pi 
producto
/     acos(1/10)\ acos(1/10)
|pi - ----------|*----------
\         2     /     2
(π−acos⁡(110)2)acos⁡(110)2\left(\pi - \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2}\right) \frac{\operatorname{acos}{\left(\frac{1}{10} \right)}}{2} 
=
(-acos(1/10) + 2*pi)*acos(1/10)
-------------------------------
               4
(−acos⁡(110)+2π)acos⁡(110)4\frac{\left(- \operatorname{acos}{\left(\frac{1}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{10} \right)}}{4} 
(-acos(1/10) + 2*pi)*acos(1/10)/4
Respuesta numérica [src] 
x1 = -69.8503528317921
x2 = 27.5390194294915
x3 = 82.4167234461513
x4 = 63.5671675246125
x5 = 2.40627820077312
x6 = 52449.6246661344
x7 = 25.868055681535
x8 = -99.7956504620567
x9 = -16.4432777207656
x10 = -27.5390194294915
x11 = 3.87690710640646
x12 = 74.6629092333384
x13 = -118.645206383595
x14 = -57.2839822174329
x15 = -33.8222047366711
x16 = 11.8310561615425
x17 = 44.7176116030738
x18 = 33.8222047366711
x19 = 40.1053900438506
x20 = -65.238131272569
x21 = -19.5848703743554
x22 = -82.4167234461513
x23 = -49.53016800462
x24 = -60.4255748710227
x25 = -90.3708725012873
x26 = 49.53016800462
x27 = 96.6540578084669
x28 = 88.6999087533309
x29 = 91.8415014069207
x30 = 62.0965386189792
x31 = -35.2928336423044
x32 = -32.1512409887146
x33 = -71.5213165797486
x34 = -25.868055681535
x35 = -79.2751307925615
x36 = 46.3885753510302
x37 = -40.1053900438506
x38 = -2.40627820077312
x39 = 84.0876871941077
x40 = -55.8133533117996
x41 = -41.576018949484
x42 = -85.5583160997411
x43 = 32.1512409887146
x44 = 98.1246867141003
x45 = 66.7087601782023
x46 = 30.6806120830813
x47 = 76.1335381389717
x48 = -68.3797239261588
x49 = -76.1335381389717
x50 = -600.779511288467
x51 = 71.5213165797486
x52 = 68.3797239261588
x53 = -93.5124651548771
x54 = -38.4344262958942
x55 = 55.8133533117996
x56 = 52.6717606582098
x57 = -54.1423895638432
x58 = 90.3708725012873
x59 = 47.8592042566636
x60 = 24.3974267759017
x61 = -91.8415014069207
x62 = 69.8503528317921
x63 = -98.1246867141003
x64 = -47.8592042566636
x65 = 10.160092413586
x66 = 0.735314452816668
x67 = 16.4432777207656
x68 = -18.1142414687221
x69 = 85.5583160997411
x70 = 77.8045018869282
x71 = -84.0876871941077
x72 = -10.160092413586
x73 = 5.54787085436292
x74 = -11.8310561615425
x75 = -24.3974267759017
x76 = 22.7264630279452
x77 = 1240.19378371515
x78 = 99.7956504620567
x79 = -46.3885753510302
x80 = 38.4344262958942
x81 = 93.5124651548771
x82 = -13.3016850671758
x83 = -77.8045018869282
x84 = 60.4255748710227
x85 = -3.87690710640646
x86 = 18.1142414687221
x87 = -62.0965386189792
x88 = 442.229249703344
x89 = 41.576018949484
x90 = 8.68946350795271
x91 = -63.5671675246125
x92 = -5.54787085436292
x93 = 54.1423895638432
x94 = 19.5848703743554
x94 = 19.5848703743554
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