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sqrt(2)*sin(x-pi/4)=-1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
  ___    /    pi\     
\/ 2 *sin|x - --| = -1
         \    4 /     
$$\sqrt{2} \sin{\left(x - \frac{\pi}{4} \right)} = -1$$
Solución detallada
Tenemos la ecuación
$$\sqrt{2} \sin{\left(x - \frac{\pi}{4} \right)} = -1$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -sqrt(2)

La ecuación se convierte en
$$\cos{\left(x + \frac{\pi}{4} \right)} = \frac{\sqrt{2}}{2}$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{4}$$
$$x + \frac{\pi}{4} = \pi n - \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n$$
$$x = \pi n - \pi$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     3*pi
x2 = ----
      2  
$$x_{2} = \frac{3 \pi}{2}$$
x2 = 3*pi/2
Suma y producto de raíces [src]
suma
3*pi
----
 2  
$$\frac{3 \pi}{2}$$
=
3*pi
----
 2  
$$\frac{3 \pi}{2}$$
producto
  3*pi
0*----
   2  
$$0 \frac{3 \pi}{2}$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = 73.8274273593601
x2 = 0.0
x3 = -18.8495559215388
x4 = -26.7035375555132
x5 = -1.5707963267949
x6 = -56.5486677646163
x7 = -95.8185759344887
x8 = -125.663706143592
x9 = -39.2699081698724
x10 = 62.8318530717959
x11 = 43.9822971502571
x12 = 87.9645943005142
x13 = 37.6991118430775
x14 = 69.1150383789755
x15 = 10.9955742875643
x16 = -50.2654824574367
x17 = 54.9778714378214
x18 = -94.2477796076938
x19 = -75.398223686155
x20 = 12.5663706143592
x21 = 23.5619449019235
x22 = 92.6769832808989
x23 = -43.9822971502571
x24 = -32.9867228626928
x25 = -31.4159265358979
x26 = -25.1327412287183
x27 = -6.28318530717959
x28 = 98.9601685880785
x29 = 36.1283155162826
x30 = -62.8318530717959
x31 = -7.85398163397448
x32 = -58.1194640914112
x33 = 213.628300444106
x34 = 31.4159265358979
x35 = 86.3937979737193
x36 = 94.2477796076938
x37 = 81.6814089933346
x38 = -89.5353906273091
x39 = -14.1371669411541
x40 = -64.4026493985908
x41 = 80.1106126665397
x42 = -100.530964914873
x43 = 205.774318810131
x44 = -12.5663706143592
x45 = 56.5486677646163
x46 = 100.530964914873
x47 = 4.71238898038469
x48 = 48.6946861306418
x49 = -69.1150383789755
x50 = -45.553093477052
x51 = 17.2787595947439
x52 = -87.9645943005142
x53 = -20.4203522483337
x54 = -83.2522053201295
x55 = 61.261056745001
x56 = -81.6814089933346
x57 = 75.398223686155
x58 = 29.845130209103
x59 = -37.6991118430775
x60 = 42.4115008234622
x61 = 18.8495559215388
x62 = -51.8362787842316
x63 = -70.6858347057703
x64 = 50.2654824574367
x65 = 67.5442420521806
x66 = 25.1327412287183
x67 = 576.482251933727
x68 = -76.9690200129499
x69 = 6.28318530717959
x69 = 6.28318530717959