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cos(3*x-pi/4)=-1

cos(3*x-pi/4)=-1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   /      pi\     
cos|3*x - --| = -1
   \      4 /
cos⁡(3x−π4)=−1\cos{\left(3 x - \frac{\pi}{4} \right)} = -1
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(3x−π4)=−1\cos{\left(3 x - \frac{\pi}{4} \right)} = -1
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
3x+π4=2πn+asin⁡(−1)3 x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}
3x+π4=2πn−asin⁡(−1)+π3 x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi
O
3x+π4=2πn−π23 x + \frac{\pi}{4} = 2 \pi n - \frac{\pi}{2}
3x+π4=2πn+3π23 x + \frac{\pi}{4} = 2 \pi n + \frac{3 \pi}{2}
, donde n es cualquier número entero
Transportemos
π4\frac{\pi}{4}
al miembro derecho de la ecuación
con el signo opuesto, en total:
3x=2πn−3π43 x = 2 \pi n - \frac{3 \pi}{4}
3x=2πn+5π43 x = 2 \pi n + \frac{5 \pi}{4}
Dividamos ambos miembros de la ecuación obtenida en
33
obtenemos la respuesta:
x1=2πn3−π4x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{4}
x2=2πn3+5π12x_{2} = \frac{2 \pi n}{3} + \frac{5 \pi}{12}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -pi 
x1 = ----
      4
x1=−π4x_{1} = - \frac{\pi}{4} 
     5*pi
x2 = ----
      12
x2=5π12x_{2} = \frac{5 \pi}{12} 
x2 = 5*pi/12
Suma y producto de raíces [src] 
suma
  pi   5*pi
- -- + ----
  4     12
−π4+5π12- \frac{\pi}{4} + \frac{5 \pi}{12} 
=
pi
--
6
π6\frac{\pi}{6} 
producto
-pi  5*pi
----*----
 4    12
−π45π12- \frac{\pi}{4} \frac{5 \pi}{12} 
=
     2
-5*pi 
------
  48
−5π248- \frac{5 \pi^{2}}{48} 
-5*pi^2/48
Respuesta numérica [src] 
x1 = 5.49778730168372
x2 = -23.8237442162572
x3 = 82.9904063510015
x4 = -36.3901147358536
x5 = 3.40339214158485
x6 = -55.2396709786605
x7 = -30.1069295143413
x8 = 36.9137137078196
x9 = -74.0892266747134
x10 = 20.1585529641208
x11 = 99.7455668949014
x12 = -76.183621730839
x13 = 24.3473430052226
x14 = 11.780972582991
x15 = -7.06858337874519
x16 = -97.1275729389989
x17 = 59.952059850908
x18 = 30.6305282141644
x19 = 91.3679863907562
x20 = 43.1968990909536
x21 = 78.8016155914877
x22 = 95.5567767146611
x23 = 24.3473427690631
x24 = -103.410758569044
x25 = -71.9948316512075
x26 = 80.8960108103565
x27 = 57.8576648042324
x28 = -42.673300271584
x29 = -61.5228562509886
x30 = 93.4623815888092
x31 = 66.2352451246023
x32 = 70.424035221104
x33 = 13.8753676452733
x34 = -28.0125344805823
x35 = -53.1452758138067
x36 = -19.6349541541781
x37 = -21.7293492019319
x38 = 53.6688746602139
x39 = -57.334066089755
x40 = -51.0508804441991
x41 = 7.59218241507256
x42 = 64.1408501561777
x43 = 55.7632697391846
x44 = -80.3724118874525
x45 = -84.5612021281352
x46 = 7208.12254390983
x47 = 32.7249233148023
x48 = 72.5184302880001
x49 = -86.6555973660817
x50 = 28.5361331323541
x51 = -34.2957196474121
x52 = 68.3296401650627
x53 = 1.30899680428975
x54 = -13.3517689381444
x55 = -65.7116463637318
x56 = 22.2529479607544
x57 = 74.6128253671092
x58 = -88.749992830708
x59 = 76.7072204634264
x60 = -67.806041389319
x61 = -92.9387830063014
x62 = 97.6511718132156
x63 = -38.4845098442049
x64 = -95.0331774856139
x65 = 18.0641575843062
x66 = -15.4461640228502
x67 = 62.0464548191486
x68 = 89.2735908908927
x69 = 47.3856892695311
x70 = -7.06858344988296
x71 = -17.5405590939996
x72 = 122.783912998323
x73 = -78.2780168019945
x74 = 9.68657750666355
x75 = -82.4668069913215
x76 = 34.8193184526325
x77 = -99.2219681230205
x78 = -32.2013245736809
x79 = 45.2912938571067
x80 = 26.4417380633665
x81 = -11.2573738326293
x82 = -40.5789049913739
x83 = -63.6172513131713
x84 = 15.9697626863592
x85 = -9.16297868279801
x86 = -59.4284611775882
x87 = 49.4800844461214
x88 = 51.5744795652683
x88 = 51.5744795652683
Gráfico
cos(3*x-pi/4)=-1 la ecuación
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