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sin(x-п/4)=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /    pi\    
sin|x - --| = 1
   \    4 /
sin⁡(x−π4)=1\sin{\left(x - \frac{\pi}{4} \right)} = 1
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(x−π4)=1\sin{\left(x - \frac{\pi}{4} \right)} = 1
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
cos⁡(x+π4)=−1\cos{\left(x + \frac{\pi}{4} \right)} = -1
Esta ecuación se reorganiza en
x+π4=πn+acos⁡(−1)x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(-1 \right)}
x+π4=πn−π+acos⁡(−1)x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}
O
x+π4=πn+πx + \frac{\pi}{4} = \pi n + \pi
x+π4=πnx + \frac{\pi}{4} = \pi n
, donde n es cualquier número entero
Transportemos
π4\frac{\pi}{4}
al miembro derecho de la ecuación
con el signo opuesto, en total:
x=πn+3π4x = \pi n + \frac{3 \pi}{4}
x=πn−π4x = \pi n - \frac{\pi}{4}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     3*pi
x1 = ----
      4
x1=3π4x_{1} = \frac{3 \pi}{4} 
x1 = 3*pi/4
Suma y producto de raíces [src] 
suma
3*pi
----
 4
3π4\frac{3 \pi}{4} 
=
3*pi
----
 4
3π4\frac{3 \pi}{4} 
producto
3*pi
----
 4
3π4\frac{3 \pi}{4} 
=
3*pi
----
 4
3π4\frac{3 \pi}{4} 
3*pi/4
Respuesta numérica [src] 
x1 = 2.3561949954224
x2 = -54.1924737827733
x3 = 40.0553062101845
x4 = 2396.24979743327
x5 = -85.6083998958857
x6 = 2.3561944237875
x7 = -73.0420287380679
x8 = -47.9092884144093
x9 = -22.7765463580839
x10 = 46.3384921428394
x11 = -54.1924731401203
x12 = 58.9048613896258
x13 = 58.9048627249819
x14 = 46.338491404885
x15 = 52.6216774604655
x16 = -35.3429168429879
x17 = -85.6083993004531
x18 = -10.210175980679
x19 = 58.9048619391766
x20 = -10.2101761334089
x21 = -79.3252134544563
x22 = -22.776547161819
x23 = -66.7588435143554
x24 = -60.4756598450723
x25 = -91.8915845718224
x26 = -41.6261028392388
x27 = 14.9225647821574
x28 = 77.7544180614729
x29 = 90.3207892898859
x30 = 71.4712323874402
x31 = 21.2057507980897
x32 = 40.0553067207441
x33 = 84.0376034201306
x34 = 197.134939701634
x35 = 65.1880471490465
x36 = 84.0376030155747
x37 = -91.8915855564091
x38 = 8.63937980518173
x39 = -35.3429164228444
x40 = 90.3207885304279
x41 = 8.63937959235237
x42 = -60.4756583156352
x43 = -47.9092893597202
x44 = 77.754418337673
x45 = 96.6039746920057
x46 = -29.0597323747788
x47 = 14.9225655707643
x48 = 33.7721211785782
x49 = -41.6261027361584
x50 = -54.1924732378437
x51 = 27.4889352646658
x52 = -79.3252147238664
x53 = 14.9225652675525
x54 = -10.2101766331647
x55 = -98.1747709320943
x56 = 21.2057499935576
x57 = 52.6216767505711
x58 = 8.6393803088358
x59 = -3.92699041690952
x60 = 77.7544176668695
x61 = 96.6039739088639
x62 = -29.0597315835865
x63 = -16.4933625746574
x64 = 90.3207887445139
x65 = 27.4889352340713
x66 = 33.7721209665242
x67 = -91.8915846950967
x68 = 52.6216776471696
x69 = -98.1747703463396
x70 = -66.758844317081
x71 = 84.0376038573287
x72 = -79.3252139950001
x73 = -73.0420295316306
x74 = 8.63938060956041
x75 = 46.3384915839933
x76 = -60.4756590721812
x77 = -41.6261021523473
x78 = -54.1924719345282
x79 = -16.4933611579594
x80 = 2.35619428158573
x81 = -98.1747702997734
x82 = -3.9269910796913
x83 = 27.4889359996335
x84 = -16.4933619191372
x85 = -47.9092875555483
x86 = 15063.1513756941
x87 = -85.6083999573295
x88 = 71.4712331571435
x89 = 40.0553058716266
x90 = 65.1880479541638
x91 = 96.6039746118957
x92 = -35.3429175657933
x93 = 33.7721205167199
x94 = -3.92699127171533
x94 = -3.92699127171533
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