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sin4x=-1

sin4x=-1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sin(4*x) = -1
$$\sin{\left(4 x \right)} = -1$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(4 x \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$4 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
O
$$4 x = 2 \pi n - \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{3 \pi}{2}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$4$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{3 \pi}{8}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      8  
$$x_{1} = - \frac{\pi}{8}$$
     3*pi
x2 = ----
      8  
$$x_{2} = \frac{3 \pi}{8}$$
x2 = 3*pi/8
Suma y producto de raíces [src]
suma
  pi   3*pi
- -- + ----
  8     8  
$$- \frac{\pi}{8} + \frac{3 \pi}{8}$$
=
pi
--
4 
$$\frac{\pi}{4}$$
producto
-pi  3*pi
----*----
 8    8  
$$- \frac{\pi}{8} \frac{3 \pi}{8}$$
=
     2
-3*pi 
------
  64  
$$- \frac{3 \pi^{2}}{64}$$
-3*pi^2/64
Respuesta numérica [src]
x1 = 48.301987014692
x2 = 27.8816348852699
x3 = -8.24668059419322
x4 = -96.2112749006757
x5 = -25.5254404172294
x6 = 93.8550806217218
x7 = -99.3528677616324
x8 = -60.0829594332135
x9 = 70.2931355951281
x10 = 32.594023666847
x11 = -17.6714587255811
x12 = -47.5165889944504
x13 = 84.4303027206186
x14 = -1.96349547006081
x15 = 100.138265970845
x16 = 78.1471173828293
x17 = 20.0276531244896
x18 = 27.8816346273068
x19 = 68.7223393336083
x20 = -41.233403301565
x21 = 12.1736716095332
x22 = 24.7400422576775
x23 = 10.6028750937315
x24 = -23.9546440698867
x25 = -31.8086255639604
x26 = 87.5718952800362
x27 = 84.4303024715116
x28 = -39.6626073053534
x29 = -75.7909227331784
x30 = -85.215700617134
x31 = 79.7179137087287
x32 = -89.9280899395631
x33 = -53.7997741489889
x34 = 34.1648201986395
x35 = 92.2842841757553
x36 = 49.8727834642995
x37 = -36.5210148980811
x38 = 46.7311907920314
x39 = -3.53429183982371
x40 = 18.4568567377593
x41 = -9.81747697788046
x42 = 4.31968985434627
x43 = -82.0741080135087
x44 = 48.3019869823087
x45 = -22.3838475557172
x46 = 21.5984495824462
x47 = 42.0188017154946
x48 = -45.9457926779855
x49 = 40.4480053155132
x50 = 90.7134878811712
x51 = 56.1559687898059
x52 = 64.0099503040047
x53 = 54.5851722404622
x54 = 2.74889373159412
x55 = -33.3794220507366
x56 = -88.3572932691129
x57 = 86.0010988906895
x58 = -16.1006622734711
x59 = -30.237829170498
x60 = -38.0918108532085
x61 = -67.9369412996327
x62 = -11.3882734788215
x63 = 57.7267651333619
x64 = -63.2245518402327
x65 = -61.6537558849751
x66 = -0.392698986134672
x67 = -77.3617191922663
x68 = -74.2201263237444
x69 = 13.7444679818906
x70 = -66.3661446973152
x71 = -55.370570621922
x72 = 71.8639320431144
x73 = 98.5674693889903
x74 = 62.4391538934323
x75 = -69.5077375714784
x76 = -367.959039667966
x77 = 5.89048630601688
x78 = -44.374996126151
x79 = 76.5763208145247
x80 = -14.5298663255924
x81 = -58.512163418571
x82 = 35.7356165577455
x83 = -83.6449044644497
x84 = -80.5033119347586
x85 = -52.2289777470169
x86 = 65.5807467157997
x87 = -91.498886148304
x88 = 26.3108384344347
x89 = 43.5895981498367
x90 = -19.2422547864247
x91 = -97.7820713166882
x91 = -97.7820713166882
Gráfico
sin4x=-1 la ecuación