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sin((-3)*x+pi/4)=(-1)/sqrt(2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   /       pi\    -1  
sin|-3*x + --| = -----
   \       4 /     ___
                 \/ 2 
$$\sin{\left(- 3 x + \frac{\pi}{4} \right)} = - \frac{1}{\sqrt{2}}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(- 3 x + \frac{\pi}{4} \right)} = - \frac{1}{\sqrt{2}}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$3 x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
O
$$3 x + \frac{\pi}{4} = \pi n + \frac{3 \pi}{4}$$
$$3 x + \frac{\pi}{4} = \pi n - \frac{\pi}{4}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$3 x = \pi n + \frac{\pi}{2}$$
$$3 x = \pi n - \frac{\pi}{2}$$
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{6}$$
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     6 
$$x_{1} = \frac{\pi}{6}$$
     pi
x2 = --
     3 
$$x_{2} = \frac{\pi}{3}$$
x2 = pi/3
Suma y producto de raíces [src]
suma
pi   pi
-- + --
6    3 
$$\frac{\pi}{6} + \frac{\pi}{3}$$
=
pi
--
2 
$$\frac{\pi}{2}$$
producto
pi pi
--*--
6  3 
$$\frac{\pi}{6} \frac{\pi}{3}$$
=
  2
pi 
---
 18
$$\frac{\pi^{2}}{18}$$
pi^2/18
Respuesta numérica [src]
x1 = 65.9734457253857
x2 = -12.0427718387609
x3 = -68.0678408277789
x4 = 44.5058959258554
x5 = -21.9911485751286
x6 = 21.9911485751286
x7 = 63.8790506229925
x8 = -15.707963267949
x9 = 42.4115008234622
x10 = 46.6002910282486
x11 = 36.1283155162826
x12 = 34.0339204138894
x13 = 10.9955742875643
x14 = 74.3510261349584
x15 = 61.7846555205993
x16 = 2.61799387799149
x17 = -5.75958653158129
x18 = -41.3643032722656
x19 = -76.4454212373516
x20 = -32.4631240870945
x21 = 54.9778714378214
x22 = 30.3687289847013
x23 = -63.8790506229925
x24 = -70.162235930172
x25 = 86.3937979737193
x26 = 70.162235930172
x27 = 98.9601685880785
x28 = -95.8185759344887
x29 = 28.2743338823081
x30 = 90.5825881785057
x31 = -1.5707963267949
x32 = 51.3126800086333
x33 = 31.9395253114962
x34 = -24.0855436775217
x35 = 84.2994028713261
x36 = 78.0162175641465
x37 = -93.7241808320955
x38 = 13.6135681655558
x39 = -3.66519142918809
x40 = 42.9350995990605
x41 = 59.6902604182061
x42 = -74.3510261349584
x43 = 72.2566310325652
x44 = 26.1799387799149
x45 = -56.025068989018
x46 = -51.8362787842316
x47 = -87.4409955249159
x48 = -61.7846555205993
x49 = 68.0678408277789
x50 = -85.3466004225227
x51 = 29.845130209103
x52 = -45.553093477052
x53 = 75.9218224617533
x54 = -38.7463093942741
x55 = -30.3687289847013
x56 = 80.1106126665397
x57 = -58.1194640914112
x58 = -49.7418836818384
x59 = -82.7286065445312
x60 = -26.1799387799149
x61 = 3.14159265358979
x62 = -100.007366139275
x63 = -72.2566310325652
x64 = -9.94837673636768
x65 = -97.9129710368819
x66 = -65.9734457253857
x67 = 38.2227106186758
x68 = -28.2743338823081
x69 = 0.523598775598299
x70 = -43.4586983746588
x71 = -86.9173967493176
x72 = -7.85398163397448
x73 = 48.6946861306418
x74 = 82.2050077689329
x75 = -79.0634151153431
x76 = 19.8967534727354
x77 = 57.5958653158129
x78 = -53.9306738866248
x79 = -382.227106186758
x80 = -59.6902604182061
x81 = 109.955742875643
x82 = -91.6297857297023
x83 = 95.2949771588904
x84 = -19.8967534727354
x85 = 40.317105721069
x86 = 24.0855436775217
x87 = 15.707963267949
x88 = -89.5353906273091
x89 = -47.6474885794452
x90 = 92.6769832808989
x91 = 17.8023583703422
x92 = -17.8023583703422
x93 = 88.4881930761125
x93 = 88.4881930761125