Sr Examen

4cos2x la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
4*cos(2*x) = 0
$$4 \cos{\left(2 x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$4 \cos{\left(2 x \right)} = 0$$
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
$$4 \cos{\left(2 x \right)} = 0$$
Dividamos ambos miembros de la ecuación en 4

La ecuación se convierte en
$$\cos{\left(2 x \right)} = 0$$
Esta ecuación se reorganiza en
$$2 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
O
$$2 x = \pi n + \frac{\pi}{2}$$
$$2 x = \pi n - \frac{\pi}{2}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{4}$$
Gráfica
Suma y producto de raíces [src]
suma
pi   3*pi
-- + ----
4     4  
$$\frac{\pi}{4} + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
producto
pi 3*pi
--*----
4   4  
$$\frac{\pi}{4} \frac{3 \pi}{4}$$
=
    2
3*pi 
-----
  16 
$$\frac{3 \pi^{2}}{16}$$
3*pi^2/16
Respuesta rápida [src]
     pi
x1 = --
     4 
$$x_{1} = \frac{\pi}{4}$$
     3*pi
x2 = ----
      4  
$$x_{2} = \frac{3 \pi}{4}$$
x2 = 3*pi/4
Respuesta numérica [src]
x1 = -41.6261026600648
x2 = 162.577419823272
x3 = 18.0641577581413
x4 = 25.9181393921158
x5 = 41.6261026600648
x6 = 40.0553063332699
x7 = 63.6172512351933
x8 = -47.9092879672443
x9 = 88.7499924639117
x10 = 96.6039740978861
x11 = 82.4668071567321
x12 = -13.3517687777566
x13 = -62.0464549083984
x14 = 44.7676953136546
x15 = -24.3473430653209
x16 = -16.4933614313464
x17 = 19.6349540849362
x18 = -3.92699081698724
x19 = 52.621676947629
x20 = -84.037603483527
x21 = -49.4800842940392
x22 = -63.6172512351933
x23 = 55.7632696012188
x24 = 91.8915851175014
x25 = 60.4756585816035
x26 = -10.2101761241668
x27 = 32.2013246992954
x28 = -85.6083998103219
x29 = 33.7721210260903
x30 = -57.3340659280137
x31 = -32.2013246992954
x32 = 30.6305283725005
x33 = -82.4668071567321
x34 = 3.92699081698724
x35 = 2.35619449019234
x36 = 16.4933614313464
x37 = 76.1836218495525
x38 = -2.35619449019234
x39 = -90.3207887907066
x40 = -46.3384916404494
x41 = -98.174770424681
x42 = 46.3384916404494
x43 = 5.49778714378214
x44 = 47.9092879672443
x45 = 99.7455667514759
x46 = -91.8915851175014
x47 = 1973.70558461779
x48 = -33.7721210260903
x49 = -19.6349540849362
x50 = -60.4756585816035
x51 = 27.4889357189107
x52 = -71.4712328691678
x53 = 84.037603483527
x54 = -76.1836218495525
x55 = -12461.9126586273
x56 = -38.484510006475
x57 = 22.776546738526
x58 = 68.329640215578
x59 = 66.7588438887831
x60 = -11.7809724509617
x61 = -27.4889357189107
x62 = 62.0464549083984
x63 = -25.9181393921158
x64 = -40.0553063332699
x65 = -5.49778714378214
x66 = 54.1924732744239
x67 = -35.3429173528852
x68 = 384.059701901352
x69 = 90.3207887907066
x70 = -55.7632696012188
x71 = 11.7809724509617
x72 = 8.63937979737193
x73 = 74.6128255227576
x74 = -54.1924732744239
x75 = -99.7455667514759
x76 = -18.0641577581413
x77 = 38.484510006475
x78 = -77.7544181763474
x79 = -79.3252145031423
x80 = 10.2101761241668
x81 = 85.6083998103219
x82 = 98.174770424681
x83 = -68.329640215578
x84 = -69.9004365423729
x85 = 49.4800842940392
x86 = 69.9004365423729
x87 = 24.3473430653209
x88 = -93.4623814442964
x89 = 77.7544181763474
x90 = 87.1791961371168
x90 = 87.1791961371168