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cos(8x)=-(1/2) la ecuación

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Ha introducido [src]

cos(8*x) = -1/2

\cos{\left(8 x \right)} = - \frac{1}{2}

Simplificar

Solución detallada

Tenemos la ecuación

\cos{\left(8 x \right)} = - \frac{1}{2}

es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en

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

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

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

8 x = \pi n - \frac{\pi}{3}

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

8

obtenemos la respuesta:

x_{1} = \frac{\pi n}{8} + \frac{\pi}{12}

x_{2} = \frac{\pi n}{8} - \frac{\pi}{24}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

pi   pi
-- + --
12   6

\frac{\pi}{12} + \frac{\pi}{6}

pi
--
4

\frac{\pi}{4}

producto

pi pi
--*--
12 6

\frac{\pi}{12} \frac{\pi}{6}

  2
pi 
---
 72

\frac{\pi^{2}}{72}

pi^2/72

Respuesta rápida [src]

     pi
x1 = --
     12

x_{1} = \frac{\pi}{12}

     pi
x2 = --
     6

x_{2} = \frac{\pi}{6}

x2 = pi/6

Respuesta numérica [src]

x1 = -11.2573736753634

x2 = -49.7418836818384

x3 = -67.8060414399797

x4 = -100.007366139275

x5 = 70.162235930172

x6 = -34.0339204138894

x7 = 78.2780169519457

x8 = -39.7935069454707

x9 = 20.1585528605345

x10 = 48.1710873550435

x11 = -41.8879020478639

x12 = 56.2868683768171

x13 = -78.801615727544

x14 = 28.012534494509

x15 = -90.8443875663049

x16 = 64.1408500107916

x17 = -12.0427718387609

x18 = -35.8665161284835

x19 = -45.8148928648512

x20 = -93.7241808320955

x21 = -56.025068989018

x22 = -19.8967534727354

x23 = 42.1497014356631

x24 = 82.2050077689329

x25 = 97.9129710368819

x26 = 60.2138591938044

x27 = -13.8753675533549

x28 = 31.9395253114962

x29 = 30.1069295969022

x30 = 6.02138591938044

x31 = 53.9306738866248

x32 = 16.2315620435473

x33 = 26.1799387799149

x34 = 100.269165527074

x35 = 24.0855436775217

x36 = -89.7971900151083

x37 = -63.8790506229925

x38 = 92.1533845053006

x39 = 12.30457122656

x40 = -81.9432083811338

x41 = -34.2957198016886

x42 = 62.3082542961976

x43 = -17.8023583703422

x44 = 75.9218224617533

x45 = 81.9432083811338

x46 = 2.0943951023932

x47 = 96.0803753222878

x48 = 88.2263936883134

x49 = -85.870199198121

x50 = 46.0766922526503

x51 = -97.9129710368819

x52 = 8.11578102177363

x53 = -79.8488132787406

x54 = -25.3945406165175

x55 = 18.3259571459405

x56 = -59.9520598060052

x57 = -87.7027949127151

x58 = 52.0980781720307

x59 = 139.539073696947

x60 = -37.9609112308767

x61 = -65.7116463375865

x62 = -52.3598775598299

x63 = 34.2957198016886

x64 = -61.7846555205993

x65 = 4.18879020478639

x66 = -23.8237442897226

x67 = 0.261799387799149

x68 = 71.9948316447661

x69 = -27.7507351067098

x70 = -1.83259571459405

x71 = 66.2352451131848

x72 = 93.9859802198946

x73 = -78.0162175641465

x74 = 50.0036830696375

x75 = -5.75958653158129

x76 = 86.1319985859202

x77 = -57.857664703612

x78 = -3.66519142918809

x79 = 68.0678408277789

x80 = 40.317105721069

x81 = 84.2994028713261

x82 = -71.733032256967

x83 = 74.0892267471593

x84 = 9.94837673636768

x85 = 90.0589894029074

x86 = 44.2440965380563

x87 = -83.7758040957278

x88 = 22.2529479629277

x89 = -96.0803753222878

x90 = -15.9697626557481

x91 = -43.720497762458

x92 = 38.2227106186758

x93 = -21.7293491873294

x93 = -21.7293491873294