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sin(-8x)=1 la ecuación

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Ha introducido [src]

sin(-8*x) = 1

\sin{\left(- 8 x \right)} = 1

Simplificar

Solución detallada

Tenemos la ecuación

\sin{\left(- 8 x \right)} = 1

es la ecuación trigonométrica más simple

Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en

\sin{\left(8 x \right)} = -1

Esta ecuación se reorganiza en

8 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}

8 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi

8 x = 2 \pi n - \frac{\pi}{2}

8 x = 2 \pi n + \frac{3 \pi}{2}

, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en

8

obtenemos la respuesta:

x_{1} = \frac{\pi n}{4} - \frac{\pi}{16}

x_{2} = \frac{\pi n}{4} + \frac{3 \pi}{16}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     -pi 
x1 = ----
      16

x_{1} = - \frac{\pi}{16}

     3*pi
x2 = ----
      16

x_{2} = \frac{3 \pi}{16}

x2 = 3*pi/16

Suma y producto de raíces [src]

suma

  pi   3*pi
- -- + ----
  16    16

- \frac{\pi}{16} + \frac{3 \pi}{16}

pi
--
8

\frac{\pi}{8}

producto

-pi  3*pi
----*----
 16   16

- \frac{\pi}{16} \frac{3 \pi}{16}

     2
-3*pi 
------
 256

- \frac{3 \pi^{2}}{256}

-3*pi^2/256

Respuesta numérica [src]

x1 = 35.9319660222562

x2 = 46.1421421198569

x3 = -77.9507678205583

x4 = -75.5945732553301

x5 = 20.2240027286092

x6 = -48.1056374564453

x7 = -30.041479714667

x8 = 13.9408174440589

x9 = -85.8047493020167

x10 = -49.676433875401

x11 = 78.3434667530406

x12 = 10.0138265643367

x13 = -74.0237768769058

x14 = -13.5481181665139

x15 = 61.8501054017707

x16 = 64.2062998954969

x17 = -89.7317401808682

x18 = -45.7494430183143

x19 = -66.1697952619188

x20 = 75.9872723223786

x21 = 50.0691328099729

x22 = -63.8136007171937

x23 = -31.6122761189326

x24 = 38.2881604409957

x25 = -5.69413671811106

x26 = 39.8589568334733

x27 = 100.334615330172

x28 = -11.9773220259965

x29 = 74.416475970512

x30 = 2.15984503691658

x31 = 12.3700210263247

x32 = -67.7405915997907

x33 = -55.9596192173894

x34 = -93.6587310305641

x35 = -1.76714585413007

x36 = -9.62112754709748

x37 = -53.6034246886308

x38 = -27.6852852969982

x39 = -8.05033113490076

x40 = -0.19634965819183

x41 = 86.1974484796933

x42 = -23.7582944364317

x43 = 83.8412539668457

x44 = 43.7859475398846

x45 = -22.1874981765728

x46 = 79.9142631764529

x47 = -70.0967860314861

x48 = 96.4076245314146

x49 = 32.0049751521835

x50 = 16.2970118612281

x51 = 37.5027624473851

x52 = 82.2704576017573

x53 = 30.4341788756115

x54 = 34.3611696009723

x55 = -88.1609438203745

x56 = 8.44303035192619

x57 = -44.1786467123442

x58 = -19.8313035467971

x59 = -4.12334030903071

x60 = 52.4253274171151

x61 = -97.5857218176355

x62 = -41.8224521319832

x63 = 60.2793090211756

x64 = 24.1509936129662

x65 = 94.051429955664

x66 = 42.2151513118095

x67 = -71.667582453276

x68 = 97.9784209053652

x69 = 53.9961237380731

x70 = -92.0879346073022

x71 = 28.8633825046593

x72 = 72.0602813485952

x73 = -52.0326282953049

x74 = -33.9684706195655

x75 = -63.0282026074152

x76 = 4942.31429267575

x77 = 57.9231145997175

x78 = -96.0149254595968

x79 = 17.8678082629997

x80 = 21.7947988856554

x81 = -26.1144888822512

x82 = 56.3523181766008

x83 = -99.9419164280609

x83 = -99.9419164280609