Sr Examen

Otras calculadoras

cos(x+2pi/3)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /    2*pi\    
cos|x + ----| = 0
   \     3  /    
$$\cos{\left(x + \frac{2 \pi}{3} \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x + \frac{2 \pi}{3} \right)} = 0$$
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
$$\cos{\left(x + \frac{2 \pi}{3} \right)} = 0$$
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
$$\sin{\left(x + \frac{\pi}{6} \right)} = 0$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
O
$$x + \frac{\pi}{6} = 2 \pi n$$
$$x + \frac{\pi}{6} = 2 \pi n + \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{6}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n - \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{5 \pi}{6}$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   5*pi
- -- + ----
  6     6  
$$- \frac{\pi}{6} + \frac{5 \pi}{6}$$
=
2*pi
----
 3  
$$\frac{2 \pi}{3}$$
producto
-pi  5*pi
----*----
 6    6  
$$- \frac{\pi}{6} \frac{5 \pi}{6}$$
=
     2
-5*pi 
------
  36  
$$- \frac{5 \pi^{2}}{36}$$
-5*pi^2/36
Respuesta rápida [src]
     -pi 
x1 = ----
      6  
$$x_{1} = - \frac{\pi}{6}$$
     5*pi
x2 = ----
      6  
$$x_{2} = \frac{5 \pi}{6}$$
x2 = 5*pi/6
Respuesta numérica [src]
x1 = 100.007366139275
x2 = -13.0899693899575
x3 = -53.9306738866248
x4 = 30.8923277602996
x5 = -63.3554518473942
x6 = 15.1843644923507
x7 = -97.9129710368819
x8 = -69.6386371545737
x9 = -25.6563400043166
x10 = 12.0427718387609
x11 = -22.5147473507269
x12 = -66.497044500984
x13 = 18.3259571459405
x14 = -3.66519142918809
x15 = 43.4586983746588
x16 = -31.9395253114962
x17 = -6.80678408277789
x18 = 78.0162175641465
x19 = 24.60914245312
x20 = 40.317105721069
x21 = 5.75958653158129
x22 = 84.2994028713261
x23 = -79.0634151153431
x24 = 96.8657734856853
x25 = -57.0722665402146
x26 = 27.7507351067098
x27 = -16.2315620435473
x28 = -88.4881930761125
x29 = 59.1666616426078
x30 = -85.3466004225227
x31 = 52.8834763354282
x32 = -47.6474885794452
x33 = -50.789081233035
x34 = 90.5825881785057
x35 = 74.8746249105567
x36 = -820.479281362534
x37 = 34.0339204138894
x38 = -101.054563690472
x39 = 8.90117918517108
x40 = 21.4675497995303
x41 = -75.9218224617533
x42 = -19.3731546971371
x43 = 46.6002910282486
x44 = 65.4498469497874
x45 = 93.7241808320955
x46 = -35.081117965086
x47 = 71.733032256967
x48 = 131.423292675173
x49 = -44.5058959258554
x50 = -82.2050077689329
x51 = -0.523598775598299
x52 = -41.3643032722656
x53 = 37.1755130674792
x54 = -94.7713783832921
x55 = -60.2138591938044
x56 = 87.4409955249159
x57 = 62.3082542961976
x58 = 2.61799387799149
x59 = -28.7979326579064
x60 = 49.7418836818384
x61 = 56.025068989018
x62 = -38.2227106186758
x63 = -9.94837673636768
x64 = -91.6297857297023
x65 = 81.1578102177363
x66 = -72.7802298081635
x67 = 68.5914396033772
x67 = 68.5914396033772