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cos(2*x-pi/4)=0

cos(2*x-pi/4)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

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

Obtenemos:
$$\cos{\left(2 x - \frac{\pi}{4} \right)} = 0$$
Esta ecuación se reorganiza en
$$2 x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$2 x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
O
$$2 x + \frac{\pi}{4} = 2 \pi n$$
$$2 x + \frac{\pi}{4} = 2 \pi n + \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$2 x = 2 \pi n - \frac{\pi}{4}$$
$$2 x = 2 \pi n + \frac{3 \pi}{4}$$
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \pi n - \frac{\pi}{8}$$
$$x_{2} = \pi n + \frac{3 \pi}{8}$$
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  pi   3*pi
- -- + ----
  8     8
$$- \frac{\pi}{8} + \frac{3 \pi}{8}$$ 
=
pi
--
4
$$\frac{\pi}{4}$$ 
producto
-pi  3*pi
----*----
 8    8
$$- \frac{\pi}{8} \frac{3 \pi}{8}$$ 
=
     2
-3*pi 
------
  64
$$- \frac{3 \pi^{2}}{64}$$ 
-3*pi^2/64
Respuesta rápida [src] 
     -pi 
x1 = ----
      8
$$x_{1} = - \frac{\pi}{8}$$ 
     3*pi
x2 = ----
      8
$$x_{2} = \frac{3 \pi}{8}$$ 
x2 = 3*pi/8
Respuesta numérica [src] 
x1 = 68.7223392972767
x2 = -82.0741080750334
x3 = 70.2931356240716
x4 = -11.388273369263
x5 = -61.6537558266997
x6 = -184.175869316702
x7 = -58.5121631731099
x8 = 18.45685683984
x9 = 76.5763209312512
x10 = 46.7311907221482
x11 = 5.89048622548086
x12 = 4.31968989868597
x13 = -19.2422550032375
x14 = 34.164820107789
x15 = -80.5033117482384
x16 = 42.0188017417635
x17 = 71.8639319508665
x18 = -96.2112750161874
x19 = 79.717913584841
x20 = 49.872783375738
x21 = 87.5718952188155
x22 = 2.74889357189107
x23 = -74.2201264410589
x24 = -88.3572933822129
x25 = -38.0918109247762
x26 = -23.9546439836222
x27 = 43.5895980685584
x28 = 26.3108384738145
x29 = -47.5165888855456
x30 = 56.1559686829176
x31 = -75.7909227678538
x32 = -53.7997741927252
x33 = 21.5984494934298
x34 = 100.138265833175
x35 = -99.3528676697772
x36 = -41.233403578366
x37 = 84.4303025652257
x38 = 9.03207887907065
x39 = -55.3705705195201
x40 = 20.0276531666349
x41 = 12.1736715326604
x42 = -69.5077374606742
x43 = -1.96349540849362
x44 = 65.5807466436869
x45 = -16.1006623496477
x46 = -67.9369411338793
x47 = 48.3019870489431
x48 = 10.6028752058656
x49 = -66.3661448070844
x50 = 86.0010988920206
x51 = -83.6449044018282
x52 = -31.8086256175967
x53 = 98.5674695063798
x54 = -39.6626072515711
x55 = 93.8550805259951
x56 = 40.4480054149686
x57 = -77.3617190946487
x58 = 57.7267650097125
x59 = 24.7400421470196
x60 = -8.24668071567321
x61 = -3.53429173528852
x62 = 62.4391539900971
x63 = -44.3749962319558
x64 = -9.8174770424681
x65 = -0.392699081698724
x66 = 78.1471172580461
x67 = 54.5851723561227
x68 = -5389.79489631499
x69 = 32.5940237809941
x70 = -36.5210145979813
x71 = 13.7444678594553
x72 = -17.6714586764426
x73 = -97.7820713429823
x74 = -91.4988860358027
x75 = 35.7356164345839
x76 = 90.7134878724053
x77 = -60.0829594999048
x78 = -30.2378292908018
x79 = 27.8816348006094
x80 = -45.9457925587507
x81 = 92.2842841992002
x82 = -33.3794219443916
x83 = -22.3838476568273
x84 = -89.9280897090078
x85 = -52.2289778659303
x86 = 64.009950316892
x87 = -25.5254403104171
x87 = -25.5254403104171
Gráfico
cos(2*x-pi/4)=0 la ecuación
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