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cos(x-pi/6)=0

cos(x-pi/6)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /    pi\    
cos|x - --| = 0
   \    6 /    
$$\cos{\left(x - \frac{\pi}{6} \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x - \frac{\pi}{6} \right)} = 0$$
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
$$\cos{\left(x - \frac{\pi}{6} \right)} = 0$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
O
$$x + \frac{\pi}{3} = 2 \pi n$$
$$x + \frac{\pi}{3} = 2 \pi n + \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{3}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      3  
$$x_{1} = - \frac{\pi}{3}$$
     2*pi
x2 = ----
      3  
$$x_{2} = \frac{2 \pi}{3}$$
x2 = 2*pi/3
Suma y producto de raíces [src]
suma
  pi   2*pi
- -- + ----
  3     3  
$$- \frac{\pi}{3} + \frac{2 \pi}{3}$$
=
pi
--
3 
$$\frac{\pi}{3}$$
producto
-pi  2*pi
----*----
 3    3  
$$- \frac{\pi}{3} \frac{2 \pi}{3}$$
=
     2
-2*pi 
------
  9   
$$- \frac{2 \pi^{2}}{9}$$
-2*pi^2/9
Respuesta numérica [src]
x1 = -32.4631240870945
x2 = 52.3598775598299
x3 = -85.870199198121
x4 = -54.4542726622231
x5 = -154.985237577096
x6 = 64.9262481741891
x7 = -95.2949771588904
x8 = 93.2005820564972
x9 = 11.5191730631626
x10 = 36.6519142918809
x11 = 2.0943951023932
x12 = 55.5014702134197
x13 = -51.3126800086333
x14 = -79.5870138909414
x15 = -4939.63084899435
x16 = -26.1799387799149
x17 = 20.943951023932
x18 = -19.8967534727354
x19 = 99.4837673636768
x20 = -76.4454212373516
x21 = -35.6047167406843
x22 = -38.7463093942741
x23 = 77.4926187885482
x24 = 80.634211442138
x25 = -73.3038285837618
x26 = 42.9350995990605
x27 = -10.471975511966
x28 = -4.18879020478639
x29 = -13.6135681655558
x30 = 27.2271363311115
x31 = -41.8879020478639
x32 = 33.5103216382911
x33 = -7.33038285837618
x34 = 58.6430628670095
x35 = -16.7551608191456
x36 = 46.0766922526503
x37 = -92.1533845053006
x38 = 71.2094334813686
x39 = 86.9173967493176
x40 = 96.342174710087
x41 = -29.3215314335047
x42 = -70.162235930172
x43 = -57.5958653158129
x44 = -48.1710873550435
x45 = 5.23598775598299
x46 = 90.0589894029074
x47 = 61.7846555205993
x48 = 17.8023583703422
x49 = 49.2182849062401
x50 = 68.0678408277789
x51 = -98.4365698124802
x52 = -82.7286065445312
x53 = 102.625360017267
x54 = 14.6607657167524
x55 = -67.0206432765823
x56 = -60.7374579694027
x57 = 24.0855436775217
x58 = 74.3510261349584
x59 = 83.7758040957278
x60 = -23.0383461263252
x61 = 8.37758040957278
x62 = -89.0117918517108
x63 = -1.0471975511966
x64 = 30.3687289847013
x65 = -63.8790506229925
x66 = 39.7935069454707
x67 = -45.0294947014537
x67 = -45.0294947014537
Gráfico
cos(x-pi/6)=0 la ecuación