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(cos(2*x)+1)/2=1/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
cos(2*x) + 1      
------------ = 1/2
     2            
$$\frac{\cos{\left(2 x \right)} + 1}{2} = \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{\cos{\left(2 x \right)} + 1}{2} = \frac{1}{2}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 1/2

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
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
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 numérica [src]
x1 = 55.7632696012188
x2 = -33.7721210260903
x3 = 3.92699081698724
x4 = -16.4933614313464
x5 = -47.9092879672443
x6 = 46.3384916404494
x7 = 16.4933614313464
x8 = -76.1836218495525
x9 = 90.3207887907066
x10 = 60.4756585816035
x11 = -99.7455667514759
x12 = -98.174770424681
x13 = -10.2101761241668
x14 = 1973.70558461779
x15 = -85.6083998103219
x16 = -2.35619449019234
x17 = -55.7632696012188
x18 = 63.6172512351933
x19 = 32.2013246992954
x20 = 18.0641577581413
x21 = 87.1791961371168
x22 = -82.4668071567321
x23 = -91.8915851175014
x24 = 77.7544181763474
x25 = -90.3207887907066
x26 = -60.4756585816035
x27 = -13.3517687777566
x28 = 91.8915851175014
x29 = -3.92699081698724
x30 = -71.4712328691678
x31 = 40.0553063332699
x32 = -25.9181393921158
x33 = 49.4800842940392
x34 = 33.7721210260903
x35 = 2.35619449019234
x36 = 47.9092879672443
x37 = 99.7455667514759
x38 = 96.6039740978861
x39 = -11.7809724509617
x40 = -62.0464549083984
x41 = -18.0641577581413
x42 = 82.4668071567321
x43 = 54.1924732744239
x44 = 5.49778714378214
x45 = -49.4800842940392
x46 = 84.037603483527
x47 = 88.7499924639117
x48 = -77.7544181763474
x49 = -46.3384916404494
x50 = 24.3473430653209
x51 = -12461.9126586273
x52 = -38.484510006475
x53 = 22.776546738526
x54 = 19.6349540849362
x55 = 44.7676953136546
x56 = 162.577419823272
x57 = 85.6083998103219
x58 = 62.0464549083984
x59 = -57.3340659280137
x60 = 76.1836218495525
x61 = 69.9004365423729
x62 = 8.63937979737193
x63 = -69.9004365423729
x64 = 68.329640215578
x65 = -63.6172512351933
x66 = 98.174770424681
x67 = 41.6261026600648
x68 = -19.6349540849362
x69 = -24.3473430653209
x70 = -93.4623814442964
x71 = -41.6261026600648
x72 = -27.4889357189107
x73 = 30.6305283725005
x74 = -84.037603483527
x75 = 10.2101761241668
x76 = 384.059701901352
x77 = 25.9181393921158
x78 = 74.6128255227576
x79 = -68.329640215578
x80 = -79.3252145031423
x81 = -40.0553063332699
x82 = 52.621676947629
x83 = 11.7809724509617
x84 = -54.1924732744239
x85 = -32.2013246992954
x86 = 27.4889357189107
x87 = 38.484510006475
x88 = -5.49778714378214
x89 = -35.3429173528852
x90 = 66.7588438887831
x90 = 66.7588438887831