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31+2*cos4x=30 la ecuación

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Ha introducido [src]

31 + 2*cos(4*x) = 30

2 \cos{\left(4 x \right)} + 31 = 30

Simplificar

Solución detallada

Tenemos la ecuación

2 \cos{\left(4 x \right)} + 31 = 30

es la ecuación trigonométrica más simple

Dividamos ambos miembros de la ecuación en 2

La ecuación se convierte en

\cos{\left(4 x \right)} = - \frac{1}{2}

Esta ecuación se reorganiza en

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

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

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

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

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

4

obtenemos la respuesta:

x_{1} = \frac{\pi n}{4} + \frac{\pi}{6}

x_{2} = \frac{\pi n}{4} - \frac{\pi}{12}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     pi
x1 = --
     6

x_{1} = \frac{\pi}{6}

     pi
x2 = --
     3

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

x2 = pi/3

Suma y producto de raíces [src]

suma

pi   pi
-- + --
6    3

\frac{\pi}{6} + \frac{\pi}{3}

pi
--
2

\frac{\pi}{2}

producto

pi pi
--*--
6  3

\frac{\pi}{6} \frac{\pi}{3}

  2
pi 
---
 18

\frac{\pi^{2}}{18}

pi^2/18

Respuesta numérica [src]

x1 = -38.2227106186758

x2 = -69.6386371545737

x3 = -35.6047167406843

x4 = -53.9306738866248

x5 = 70.162235930172

x6 = 75.9218224617533

x7 = 22.5147473507269

x8 = -42.9350995990605

x9 = 96.342174710087

x10 = -68.0678408277789

x11 = 2.0943951023932

x12 = -41.8879020478639

x13 = -85.870199198121

x14 = 66.497044500984

x15 = 0.523598775598299

x16 = 4.18879020478639

x17 = 84.2994028713261

x18 = -16.2315620435473

x19 = -64.9262481741891

x20 = 38.2227106186758

x21 = 26.1799387799149

x22 = 40.317105721069

x23 = 52.3598775598299

x24 = -92.1533845053006

x25 = 49.7418836818384

x26 = 93.7241808320955

x27 = 63.8790506229925

x28 = -25.6563400043166

x29 = -34.0339204138894

x30 = 27.7507351067098

x31 = 68.0678408277789

x32 = -13.6135681655558

x33 = -57.5958653158129

x34 = -78.0162175641465

x35 = -19.8967534727354

x36 = -71.733032256967

x37 = 8.37758040957278

x38 = 44.5058959258554

x39 = 53.9306738866248

x40 = 48.1710873550435

x41 = 88.4881930761125

x42 = 92.1533845053006

x43 = -47.6474885794452

x44 = 78.0162175641465

x45 = 60.2138591938044

x46 = -5.75958653158129

x47 = -83.7758040957278

x48 = -61.7846555205993

x49 = -90.0589894029074

x50 = -79.0634151153431

x51 = -82.2050077689329

x52 = -39.7935069454707

x53 = 5.75958653158129

x54 = -31.9395253114962

x55 = 46.0766922526503

x56 = -46.0766922526503

x57 = 12.0427718387609

x58 = 82.2050077689329

x59 = -79.5870138909414

x60 = 30.3687289847013

x61 = -60.2138591938044

x62 = -93.7241808320955

x63 = -75.9218224617533

x64 = 19.8967534727354

x65 = -49.7418836818384

x66 = -100.007366139275

x67 = 34.0339204138894

x68 = -86.9173967493176

x69 = -97.9129710368819

x70 = 31.9395253114962

x71 = 9.94837673636768

x72 = -17.8023583703422

x73 = -56.025068989018

x74 = -3.66519142918809

x75 = 24.0855436775217

x76 = 74.3510261349584

x77 = 56.025068989018

x78 = 100.007366139275

x79 = 97.9129710368819

x80 = 41.8879020478639

x81 = -12.0427718387609

x82 = 85.870199198121

x83 = -27.7507351067098

x84 = 90.0589894029074

x85 = 62.3082542961976

x86 = -2.0943951023932

x87 = -93.2005820564972

x88 = -24.0855436775217

x89 = 43.4586983746588

x90 = 71.733032256967

x91 = -63.8790506229925

x92 = 16.2315620435473

x93 = -9.94837673636768

x94 = 18.3259571459405

x94 = 18.3259571459405