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6cos(2x) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
6*cos(2*x) = 0
6cos⁡(2x)=06 \cos{\left(2 x \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
6cos⁡(2x)=06 \cos{\left(2 x \right)} = 0
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
6cos⁡(2x)=06 \cos{\left(2 x \right)} = 0
Dividamos ambos miembros de la ecuación en 6

La ecuación se convierte en
cos⁡(2x)=0\cos{\left(2 x \right)} = 0
Esta ecuación se reorganiza en
2x=πn+acos⁡(0)2 x = \pi n + \operatorname{acos}{\left(0 \right)}
2x=πn−π+acos⁡(0)2 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}
O
2x=πn+π22 x = \pi n + \frac{\pi}{2}
2x=πn−π22 x = \pi n - \frac{\pi}{2}
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
22
obtenemos la respuesta:
x1=πn2+π4x_{1} = \frac{\pi n}{2} + \frac{\pi}{4}
x2=πn2−π4x_{2} = \frac{\pi n}{2} - \frac{\pi}{4}
Gráfica
0-80-60-40-2020406080-100100-1010
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
pi   3*pi
-- + ----
4     4
π4+3π4\frac{\pi}{4} + \frac{3 \pi}{4} 
=
pi
π\pi 
producto
pi 3*pi
--*----
4   4
π43π4\frac{\pi}{4} \frac{3 \pi}{4} 
=
    2
3*pi 
-----
  16
3π216\frac{3 \pi^{2}}{16} 
3*pi^2/16
Respuesta rápida [src] 
     pi
x1 = --
     4
x1=π4x_{1} = \frac{\pi}{4} 
     3*pi
x2 = ----
      4
x2=3π4x_{2} = \frac{3 \pi}{4} 
x2 = 3*pi/4
Respuesta numérica [src] 
x1 = 18.0641577581413
x2 = -46.3384916404494
x3 = 52.621676947629
x4 = 49.4800842940392
x5 = 33.7721210260903
x6 = 38.484510006475
x7 = -2.35619449019234
x8 = -69.9004365423729
x9 = 32.2013246992954
x10 = 46.3384916404494
x11 = 60.4756585816035
x12 = -98.174770424681
x13 = -82.4668071567321
x14 = 30.6305283725005
x15 = -91.8915851175014
x16 = 47.9092879672443
x17 = 162.577419823272
x18 = 54.1924732744239
x19 = 19.6349540849362
x20 = 11.7809724509617
x21 = 69.9004365423729
x22 = -19.6349540849362
x23 = 68.329640215578
x24 = 384.059701901352
x25 = -57.3340659280137
x26 = -24.3473430653209
x27 = -85.6083998103219
x28 = -47.9092879672443
x29 = 16.4933614313464
x30 = -32.2013246992954
x31 = 25.9181393921158
x32 = 40.0553063332699
x33 = -33.7721210260903
x34 = 44.7676953136546
x35 = 8.63937979737193
x36 = 27.4889357189107
x37 = -79.3252145031423
x38 = 24.3473430653209
x39 = -25.9181393921158
x40 = 22.776546738526
x41 = -13.3517687777566
x42 = -16.4933614313464
x43 = -62.0464549083984
x44 = -49.4800842940392
x45 = -5.49778714378214
x46 = 87.1791961371168
x47 = 10.2101761241668
x48 = 76.1836218495525
x49 = 99.7455667514759
x50 = 90.3207887907066
x51 = -35.3429173528852
x52 = -3.92699081698724
x53 = -55.7632696012188
x54 = -93.4623814442964
x55 = -40.0553063332699
x56 = -68.329640215578
x57 = 77.7544181763474
x58 = 91.8915851175014
x59 = -99.7455667514759
x60 = 66.7588438887831
x61 = -38.484510006475
x62 = 55.7632696012188
x63 = -41.6261026600648
x64 = -1152.17910570406
x65 = -54.1924732744239
x66 = 2.35619449019234
x67 = -90.3207887907066
x68 = -76.1836218495525
x69 = -77.7544181763474
x70 = 3.92699081698724
x71 = 5.49778714378214
x72 = -18.0641577581413
x73 = -84.037603483527
x74 = -11.7809724509617
x75 = 88.7499924639117
x76 = 74.6128255227576
x77 = -10.2101761241668
x78 = -71.4712328691678
x79 = -27.4889357189107
x80 = 82.4668071567321
x81 = 63.6172512351933
x82 = 62.0464549083984
x83 = 85.6083998103219
x84 = 41.6261026600648
x85 = 98.174770424681
x86 = 96.6039740978861
x87 = -63.6172512351933
x88 = 84.037603483527
x89 = -60.4756585816035
x89 = -60.4756585816035
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