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

cos(3*x+pi/4)=1 la ecuación

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Solución numérica:

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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=πn+acos⁡(1)3 x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(1 \right)}
3x+π4=πn−π+acos⁡(1)3 x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}
O
3x+π4=πn3 x + \frac{\pi}{4} = \pi n
3x+π4=πn−π3 x + \frac{\pi}{4} = \pi n - \pi
, donde n es cualquier número entero
Transportemos
π4\frac{\pi}{4}
al miembro derecho de la ecuación
con el signo opuesto, en total:
3x=πn−π43 x = \pi n - \frac{\pi}{4}
3x=πn−5π43 x = \pi n - \frac{5 \pi}{4}
Dividamos ambos miembros de la ecuación obtenida en
33
obtenemos la respuesta:
x1=πn3−π12x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}
x2=πn3−5π12x_{2} = \frac{\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 = ----
      12
x1=−π12x_{1} = - \frac{\pi}{12} 
     7*pi
x2 = ----
      12
x2=7π12x_{2} = \frac{7 \pi}{12} 
x2 = 7*pi/12
Suma y producto de raíces [src] 
suma
  pi   7*pi
- -- + ----
  12    12
−π12+7π12- \frac{\pi}{12} + \frac{7 \pi}{12} 
=
pi
--
2
π2\frac{\pi}{2} 
producto
-pi  7*pi
----*----
 12   12
−π127π12- \frac{\pi}{12} \frac{7 \pi}{12} 
=
     2
-7*pi 
------
 144
−7π2144- \frac{7 \pi^{2}}{144} 
-7*pi^2/144
Respuesta numérica [src] 
x1 = -79.8488131592722
x2 = -77.754418173027
x3 = -84.0376034467285
x4 = 83.5140048698821
x5 = 41.6261028270884
x6 = -27.4889358489075
x7 = -23.3001456762164
x8 = 22.776546590816
x9 = 68.8532388987811
x10 = 98.1747705003344
x11 = 1.83259582654535
x12 = -56.8104666995589
x13 = 85.6083999786327
x14 = 60.4756584639651
x15 = -46.338491477851
x16 = -17.0169598154477
x17 = 56.2868683516111
x18 = 87.7027950673316
x19 = -75.6600231301207
x20 = -54.7160723293869
x21 = 81.4196097217387
x22 = 3.92699087937343
x23 = -67.282442825287
x24 = -2.35619432508569
x25 = -40.0553062829428
x26 = -63.0936524529806
x27 = 89.7971901412795
x28 = -98.6983693725854
x29 = 24.8709417730346
x30 = 70.9476342621612
x31 = 47.9092880405714
x32 = 64.6644486247336
x33 = 29.0597318189733
x34 = -73.565628072841
x35 = 33.2485219176551
x36 = 66.7588437353286
x37 = 35.3429173442365
x38 = -8.63937976312198
x39 = 16.4933613073298
x40 = -96.6039740062802
x41 = 12.3045711904648
x42 = -21.2057505517014
x43 = -4.45058942523121
x44 = -42.1497013315978
x45 = 54.1924733268043
x46 = -81.9432085118597
x47 = 58.3812634019502
x48 = 43.7204979127911
x49 = -92.4151837241356
x50 = -6.54498455422269
x51 = 45.8148929841626
x52 = -60.9992570445465
x53 = -25.3945407708726
x54 = -44.2440963977607
x55 = 996.670269461816
x56 = 37.4373125852592
x57 = 98.1747708342799
x58 = -31.6777259700848
x59 = 18.5877563828871
x60 = 26.9653372188605
x61 = 75.1364243851404
x62 = -94.5095788398214
x63 = 62.5700535371728
x64 = 20.6821514738289
x65 = 14.3989662433122
x66 = -0.261799242243068
x67 = -10.7337752933767
x68 = -35.8665159744819
x69 = 79.3252144373659
x70 = 93.9859802353392
x71 = -86.1319984903058
x72 = 8.11578143536524
x73 = -33.7721210085797
x74 = -88.226393553756
x75 = 6.02138631959352
x76 = 39.5317077228614
x77 = -19.1113553451203
x78 = 91.8915852008749
x79 = 6.02138588891627
x80 = -65.1880476917563
x81 = -69.3768379240664
x82 = -48.4328865742642
x83 = -29.5833309149496
x84 = -90.3207886311762
x85 = 10.2101761577243
x86 = -50.5272816960703
x87 = -37.9609112985474
x88 = 100.269165513477
x89 = 50.0036830650961
x90 = -71.4712330047311
x91 = -52.6216768808878
x91 = -52.6216768808878
Gráfico
cos(3*x+pi/4)=1 la ecuación
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