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cos(x/8+pi/4)=1

cos(x/8+pi/4)=1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   /x   pi\    
cos|- + --| = 1
   \8   4 /
$$\cos{\left(\frac{x}{8} + \frac{\pi}{4} \right)} = 1$$
Simplificar
Solución detallada
Tenemos la ecuación
$$\cos{\left(\frac{x}{8} + \frac{\pi}{4} \right)} = 1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{x}{8} + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$\frac{x}{8} + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
O
$$\frac{x}{8} + \frac{\pi}{4} = \pi n$$
$$\frac{x}{8} + \frac{\pi}{4} = \pi n - \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$\frac{x}{8} = \pi n - \frac{\pi}{4}$$
$$\frac{x}{8} = \pi n - \frac{5 \pi}{4}$$
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{1}{8}$$
obtenemos la respuesta:
$$x_{1} = 8 \pi n - 2 \pi$$
$$x_{2} = 8 \pi n - 10 \pi$$
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
-2*pi + 14*pi
$$- 2 \pi + 14 \pi$$ 
=
12*pi
$$12 \pi$$ 
producto
-2*pi*14*pi
$$- 2 \pi 14 \pi$$ 
=
      2
-28*pi
$$- 28 \pi^{2}$$ 
-28*pi^2
Respuesta rápida [src] 
x1 = -2*pi
$$x_{1} = - 2 \pi$$ 
x2 = 14*pi
$$x_{2} = 14 \pi$$ 
x2 = 14*pi
Respuesta numérica [src] 
x1 = -6.28318512418657
x2 = 43.9822904462094
x3 = -6.28318895482682
x4 = -56.5486683532657
x5 = -56.5486678307325
x6 = -56.5486638231441
x7 = 94.2477769906178
x8 = -6.28318601724157
x9 = 43.9823020765976
x10 = -56.5486701441855
x11 = -56.5486649267485
x12 = 43.9822971694769
x13 = -56.5486718735468
x14 = 94.2477796093523
x15 = -56.5486713869336
x16 = -6.28318899323361
x17 = -6.28318772342667
x18 = -6.28318256385204
x19 = -6.28318690506942
x20 = 43.9822997968378
x21 = 94.2477755202581
x22 = -106.814146097798
x23 = 43.9822954991962
x24 = 43.9822981362514
x25 = 94.2477861819348
x26 = -56.5486708047995
x27 = -6.28318119421106
x28 = -6.28318934569098
x29 = -6.28318131104164
x30 = 94.2477786570642
x31 = 94.2477762226776
x32 = -106.814146259303
x33 = -106.814147439206
x34 = 43.9822982995603
x35 = 94.2477758051249
x36 = -6.28318843399251
x37 = -56.5486776860704
x38 = 43.9823012482613
x39 = -106.814151074373
x40 = 94.2477821554189
x41 = -106.814159376448
x42 = 43.9822946326014
x43 = 43.9822963195339
x44 = -56.548664295998
x45 = -6.28318940114689
x46 = -6.2831937811219
x47 = -157.079634939341
x48 = 43.9822930845907
x49 = -56.5486674525757
x50 = -56.5486692478789
x51 = 94.2477777842769
x52 = 94.2477784203741
x53 = -6.28318191311595
x54 = -56.54867580794
x55 = -56.5486715149823
x56 = -106.814147291951
x57 = 43.9823040449486
x58 = -6.2831833402855
x59 = -106.814146347399
x60 = -6.28318602316776
x61 = 43.9822934040677
x62 = -6.28318181321916
x63 = 194.778751454351
x64 = -307.876085800017
x65 = -56.5486656889023
x66 = -6.28318420227934
x67 = 43.9822930796088
x68 = -6.28318471346981
x69 = 94.2477755694512
x70 = -56.5486636427642
x71 = 43.9823009709802
x72 = 43.9823005247175
x73 = 94.2477804739555
x74 = 43.982300466748
x75 = -6.28318143493258
x76 = 43.9822990068294
x77 = -6.28318210049443
x78 = -56.5486717708719
x79 = -56.5486654842072
x80 = 43.982293939466
x81 = -6.28318735173461
x82 = 194.778747772782
x83 = -56.5486665416948
x84 = -56.5486638449637
x85 = 43.9822936235391
x86 = 94.2477763156869
x87 = 43.9823011900812
x88 = 43.9822954389537
x89 = -106.814146682021
x90 = -56.5486647535881
x91 = 94.2477813525311
x92 = -56.5486700775614
x92 = -56.5486700775614
Gráfico
cos(x/8+pi/4)=1 la ecuación
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