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cos(x+(п/3))*cos(x-(п/3))=-1/2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /    pi\    /    pi\       
cos|x + --|*cos|x - --| = -1/2
   \    3 /    \    3 /       
$$\cos{\left(x - \frac{\pi}{3} \right)} \cos{\left(x + \frac{\pi}{3} \right)} = - \frac{1}{2}$$
Gráfica
Suma y producto de raíces [src]
suma
  2*pi   pi   pi   2*pi
- ---- - -- + -- + ----
   3     3    3     3  
$$\left(\left(- \frac{2 \pi}{3} - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \frac{2 \pi}{3}$$
=
0
$$0$$
producto
-2*pi -pi  pi 2*pi
-----*----*--*----
  3    3   3   3  
$$\frac{2 \pi}{3} \frac{\pi}{3} \cdot - \frac{2 \pi}{3} \left(- \frac{\pi}{3}\right)$$
=
    4
4*pi 
-----
  81 
$$\frac{4 \pi^{4}}{81}$$
4*pi^4/81
Respuesta rápida [src]
     -2*pi
x1 = -----
       3  
$$x_{1} = - \frac{2 \pi}{3}$$
     -pi 
x2 = ----
      3  
$$x_{2} = - \frac{\pi}{3}$$
     pi
x3 = --
     3 
$$x_{3} = \frac{\pi}{3}$$
     2*pi
x4 = ----
      3  
$$x_{4} = \frac{2 \pi}{3}$$
x4 = 2*pi/3
Respuesta numérica [src]
x1 = -93.2005820564972
x2 = -68.0678408277789
x3 = -79.5870138909414
x4 = 63.8790506229925
x5 = 82.7286065445312
x6 = -85.870199198121
x7 = -4.18879020478639
x8 = 74.3510261349584
x9 = 61.7846555205993
x10 = -35.6047167406843
x11 = 2.0943951023932
x12 = 33.5103216382911
x13 = -76.4454212373516
x14 = -32.4631240870945
x15 = 30.3687289847013
x16 = -63.8790506229925
x17 = 39.7935069454707
x18 = -70.162235930172
x19 = 70.162235930172
x20 = 38.7463093942741
x21 = 76.4454212373516
x22 = -39.7935069454707
x23 = -77.4926187885482
x24 = -294.262511886244
x25 = -96.342174710087
x26 = 85.870199198121
x27 = -296.356906988637
x28 = 98.4365698124802
x29 = -24.0855436775217
x30 = 20.943951023932
x31 = -90.0589894029074
x32 = -41.8879020478639
x33 = 60.7374579694027
x34 = 90.0589894029074
x35 = -2.0943951023932
x36 = 41.8879020478639
x37 = 26.1799387799149
x38 = 55.5014702134197
x39 = 79.5870138909414
x40 = -61.7846555205993
x41 = 68.0678408277789
x42 = -13.6135681655558
x43 = -55.5014702134197
x44 = -30.3687289847013
x45 = -1032.53678547985
x46 = -14.6607657167524
x47 = 77.4926187885482
x48 = -26.1799387799149
x49 = 8.37758040957278
x50 = 52.3598775598299
x51 = -46.0766922526503
x52 = -33.5103216382911
x53 = 16.7551608191456
x54 = -60.7374579694027
x55 = -378.038315981972
x56 = -99.4837673636768
x57 = -27.2271363311115
x58 = -5.23598775598299
x59 = 96.342174710087
x60 = -11.5191730631626
x61 = -83.7758040957278
x62 = -54.4542726622231
x63 = 19.8967534727354
x64 = 48.1710873550435
x65 = -49.2182849062401
x66 = -10.471975511966
x67 = 4.18879020478639
x68 = 32.4631240870945
x69 = 11.5191730631626
x70 = 83.7758040957278
x71 = -71.2094334813686
x72 = -19.8967534727354
x73 = 54.4542726622231
x74 = 99.4837673636768
x75 = 92.1533845053006
x76 = -48.1710873550435
x77 = 46.0766922526503
x78 = 24.0855436775217
x79 = 10.471975511966
x80 = 17.8023583703422
x81 = -17.8023583703422
x82 = -57.5958653158129
x83 = -92.1533845053006
x84 = 1515.29485658148
x85 = -98.4365698124802
x85 = -98.4365698124802