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cos(4*x)=1

cos(4*x)=1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(4*x) = 1
$$\cos{\left(4 x \right)} = 1$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(4 x \right)} = 1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$4 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
O
$$4 x = \pi n$$
$$4 x = \pi n - \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$4$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{4}$$
$$x_{2} = \frac{\pi n}{4} - \frac{\pi}{4}$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
x2 = pi/2
Suma y producto de raíces [src]
suma
pi
--
2 
$$\frac{\pi}{2}$$
=
pi
--
2 
$$\frac{\pi}{2}$$
producto
  pi
0*--
  2 
$$0 \frac{\pi}{2}$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = -72.2566309100272
x2 = 95.8185756842062
x3 = -53.4070752253874
x4 = 28.2743338652921
x5 = -29.8451301000724
x6 = 48.6946860958663
x7 = 70.6858346557926
x8 = -344.004395625893
x9 = -36.128315427252
x10 = 56.5486676469942
x11 = -1.57079642013166
x12 = 4.71238898608896
x13 = -97.3893725907902
x14 = 89.5353906153414
x15 = 95.8185760424586
x16 = 0.0
x17 = -50.2654823342013
x18 = 59.690260541069
x19 = 94.247779609353
x20 = -20.4203521774723
x21 = -6.28318518328035
x22 = 117.809724442492
x23 = -81.6814090370675
x24 = 14.1371670778185
x25 = 65.9734457525462
x26 = -61.2610566398387
x27 = 81.6814091152362
x28 = -28.2743337586152
x29 = -7.85398150696156
x30 = -89.5353907315491
x31 = -67.5442421539445
x32 = -51.8362786915081
x33 = 7.85398173011892
x34 = 42.4115007365289
x35 = -97.3893723711949
x36 = -42.4115007432387
x37 = -43.9822971747455
x38 = 67.5442420634706
x39 = -83.2522051669813
x40 = 86.3937978937855
x41 = -75.3982237985682
x42 = -15.7079632962205
x43 = -80.1106125854791
x44 = 34.5575190717885
x45 = 64.4026493150839
x46 = 87.9645943351391
x47 = 36.1283154718409
x48 = -86.3937978789102
x49 = -94.247779486083
x50 = 51.8362788866811
x51 = -87.9645943594276
x52 = -59.6902604569585
x53 = -37.6991118766796
x54 = -58.1194640062544
x55 = 50.2654824463816
x56 = 72.2566310277248
x57 = -45.5530935761698
x58 = -64.402649310466
x59 = 29.8451303084991
x60 = 6.28318528443138
x61 = -65.9734457653935
x62 = -39.2699081045218
x63 = 12.5663704969137
x64 = -100.530965206253
x65 = 72.256630710694
x66 = 20.4203521581227
x67 = 1.57079638652515
x68 = 26.7035375390573
x69 = 45.5530935075531
x70 = -9.42477807759933
x71 = -31.4159266517141
x72 = 15.7079633917898
x73 = 21.9911485851564
x74 = -21.9911485864927
x75 = 37.6991119665793
x76 = -14.1371668484631
x77 = 23.5619449483644
x78 = -95.818575868455
x79 = 43.9822971692691
x80 = 78.5398162225044
x81 = 92.6769832182628
x82 = -23.5619449982306
x83 = -73.8274272808521
x84 = -1.57079626356835
x85 = 100.530964798296
x86 = 73.8274274646672
x87 = -17.2787595621355
x87 = -17.2787595621355
Gráfico
cos(4*x)=1 la ecuación