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8*sin^2(((7*pi)/12)+x)-2*sqrt(3)*cos(2x)=5 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
     2/7*pi    \       ___             
8*sin |---- + x| - 2*\/ 3 *cos(2*x) = 5
      \ 12     /                       
$$8 \sin^{2}{\left(x + \frac{7 \pi}{12} \right)} - 2 \sqrt{3} \cos{\left(2 x \right)} = 5$$
Gráfica
Suma y producto de raíces [src]
suma
  5*pi   pi   7*pi   11*pi
- ---- - -- + ---- + -----
   12    12    12      12 
$$\left(\left(- \frac{5 \pi}{12} - \frac{\pi}{12}\right) + \frac{7 \pi}{12}\right) + \frac{11 \pi}{12}$$
=
pi
$$\pi$$
producto
-5*pi -pi  7*pi 11*pi
-----*----*----*-----
  12   12   12    12 
$$\frac{11 \pi}{12} \frac{7 \pi}{12} \cdot - \frac{5 \pi}{12} \left(- \frac{\pi}{12}\right)$$
=
      4
385*pi 
-------
 20736 
$$\frac{385 \pi^{4}}{20736}$$
385*pi^4/20736
Respuesta rápida [src]
     -5*pi
x1 = -----
       12 
$$x_{1} = - \frac{5 \pi}{12}$$
     -pi 
x2 = ----
      12 
$$x_{2} = - \frac{\pi}{12}$$
     7*pi
x3 = ----
      12 
$$x_{3} = \frac{7 \pi}{12}$$
     11*pi
x4 = -----
       12 
$$x_{4} = \frac{11 \pi}{12}$$
x4 = 11*pi/12
Respuesta numérica [src]
x1 = -23.3001455141243
x2 = 78.2780169519457
x3 = 90.8443875663049
x4 = 56.2868683768171
x5 = -73.565627971561
x6 = 28.012534494509
x7 = -42.1497014356631
x8 = -66.2352451131848
x9 = 18.5877565337396
x10 = -35.8665161284835
x11 = -88.2263936883134
x12 = 58.3812634792103
x13 = -20.1585528605345
x14 = 59.4284610304069
x15 = -7.59218224617533
x16 = -44.2440965380563
x17 = -51.5744793964324
x18 = -1583.62449679705
x19 = 23.8237442897226
x20 = 42.6733002112614
x21 = -0.261799387799149
x22 = -13.8753675533549
x23 = 30.1069295969022
x24 = -50.5272818452358
x25 = 6.02138591938044
x26 = -17.0169602069447
x27 = -9.68657734856853
x28 = -31.6777259236971
x29 = 100.269165527074
x30 = -45.2912940892529
x31 = 12.30457122656
x32 = -81.9432083811338
x33 = 43.720497762458
x34 = 84.5612022591253
x35 = -95.5567765466895
x36 = 64.6644487863899
x37 = 96.0803753222878
x38 = 40.5789051088682
x39 = 8.11578102177363
x40 = 67.8060414399797
x41 = -79.8488132787406
x42 = -97.6511716490827
x43 = -59.9520598060052
x44 = -1.30899693899575
x45 = 62.5700536839967
x46 = 52.0980781720307
x47 = -91.3679863419031
x48 = 21.7293491873294
x49 = -28.5361332701073
x50 = -37.9609112308767
x51 = -86.1319985859202
x52 = -94.5095789954929
x53 = 34.2957198016886
x54 = 89.7971900151083
x55 = 81.4196096055355
x56 = 15.4461638801498
x57 = 37.4373124552784
x58 = 71.9948316447661
x59 = 14.3989663289532
x60 = 93.9859802198946
x61 = 36.3901149040818
x62 = 50.0036830696375
x63 = -57.857664703612
x64 = -89.27359123951
x65 = 20.6821516361328
x66 = -64.1408500107916
x67 = 87.7027949127151
x68 = -75.6600230739542
x69 = -53.6688744988256
x70 = 45.8148928648512
x71 = 74.0892267471593
x72 = 127.496301858186
x73 = -6.54498469497874
x74 = 80.3724120543389
x75 = 86.6555973615185
x76 = 1.83259571459405
x77 = -72.5184304203644
x78 = -15.9697626557481
x79 = 65.7116463375865
x80 = -29.5833308213039
x81 = -22.2529479629277
x82 = -67.2824426643814
x82 = -67.2824426643814