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cos(2*x-pi/4)=1/(sqrt(2)) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /      pi\     1  
cos|2*x - --| = -----
   \      4 /     ___
                \/ 2 
$$\cos{\left(2 x - \frac{\pi}{4} \right)} = \frac{1}{\sqrt{2}}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(2 x - \frac{\pi}{4} \right)} = \frac{1}{\sqrt{2}}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$2 x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$2 x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
O
$$2 x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{4}$$
$$2 x + \frac{\pi}{4} = 2 \pi n + \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$2 x = 2 \pi n$$
$$2 x = 2 \pi n + \frac{\pi}{2}$$
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \frac{\pi}{4}$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     pi
x2 = --
     4 
$$x_{2} = \frac{\pi}{4}$$
x2 = pi/4
Suma y producto de raíces [src]
suma
pi
--
4 
$$\frac{\pi}{4}$$
=
pi
--
4 
$$\frac{\pi}{4}$$
producto
  pi
0*--
  4 
$$0 \frac{\pi}{4}$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = -97.3893722612836
x2 = -43.9822971502571
x3 = -2.35619449019234
x4 = 41.6261026600648
x5 = -193.99334635917
x6 = 56.5486677646163
x7 = -84.037603483527
x8 = 28.2743338823081
x9 = -81.6814089933346
x10 = -96.6039740978861
x11 = -15.707963267949
x12 = -55.7632696012188
x13 = 72.2566310325652
x14 = 57.3340659280137
x15 = -103.672557568463
x16 = -52.621676947629
x17 = -53.4070751110265
x18 = -247.400421470196
x19 = 100.530964914873
x20 = -9.42477796076938
x21 = 82.4668071567321
x22 = -11.7809724509617
x23 = 60.4756585816035
x24 = 38.484510006475
x25 = -21.9911485751286
x26 = 76.1836218495525
x27 = -78.5398163397448
x28 = -77.7544181763474
x29 = -91.106186954104
x30 = -8.63937979737193
x31 = 69.9004365423729
x32 = -74.6128255227576
x33 = -72.2566310325652
x34 = 32.2013246992954
x35 = 50.2654824574367
x36 = 40.8407044966673
x37 = 22.776546738526
x38 = -25.1327412287183
x39 = 2243.88255282651
x40 = -30.6305283725005
x41 = 63.6172512351933
x42 = -87.9645943005142
x43 = -18.0641577581413
x44 = -62.0464549083984
x45 = 13.3517687777566
x46 = 0.0
x47 = 47.9092879672443
x48 = -65.9734457253857
x49 = 47.1238898038469
x50 = 18.8495559215388
x51 = 84.8230016469244
x52 = 91.106186954104
x53 = 6.28318530717959
x54 = -47.1238898038469
x55 = 94.2477796076938
x56 = 54.1924732744239
x57 = 65.9734457253857
x58 = -99.7455667514759
x59 = 19.6349540849362
x60 = 21.9911485751286
x61 = 85.6083998103219
x62 = 78.5398163397448
x63 = -68.329640215578
x64 = 87.9645943005142
x65 = 12.5663706143592
x66 = -3.14159265358979
x67 = 3.92699081698724
x68 = -37.6991118430775
x69 = 79.3252145031423
x70 = 10.2101761241668
x71 = -33.7721210260903
x72 = -46.3384916404494
x73 = 43.9822971502571
x74 = -59.6902604182061
x75 = -75.398223686155
x76 = 25.9181393921158
x77 = -24.3473430653209
x78 = -69.1150383789755
x79 = 91.8915851175014
x80 = -90.3207887907066
x81 = 4377.02396461398
x82 = 62.8318530717959
x83 = -40.0553063332699
x84 = 98.174770424681
x85 = -106.028752058656
x86 = 34.5575191894877
x87 = -31.4159265358979
x88 = 35.3429173528852
x88 = 35.3429173528852