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(2cos(x)^2-sin(x)-1)/log2(sin(x))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
     2                    
2*cos (x) - sin(x) - 1    
---------------------- = 0
    /log(sin(x))\         
    |-----------|         
    \   log(2)  /         
$$\frac{\left(- \sin{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right) - 1}{\frac{1}{\log{\left(2 \right)}} \log{\left(\sin{\left(x \right)} \right)}} = 0$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     pi
x2 = --
     6 
$$x_{2} = \frac{\pi}{6}$$
     5*pi
x3 = ----
      6  
$$x_{3} = \frac{5 \pi}{6}$$
x3 = 5*pi/6
Suma y producto de raíces [src]
suma
  pi   pi   5*pi
- -- + -- + ----
  2    6     6  
$$\left(- \frac{\pi}{2} + \frac{\pi}{6}\right) + \frac{5 \pi}{6}$$
=
pi
--
2 
$$\frac{\pi}{2}$$
producto
-pi  pi 5*pi
----*--*----
 2   6   6  
$$\frac{5 \pi}{6} \cdot - \frac{\pi}{2} \frac{\pi}{6}$$
=
     3
-5*pi 
------
  72  
$$- \frac{5 \pi^{3}}{72}$$
-5*pi^3/72
Respuesta numérica [src]
x1 = 10.9955739715227 + 2.24471791451794e-7*i
x2 = 23.561945200925 - 1.79244197756465e-8*i
x3 = -32.9867231740263 + 2.64699671806025e-7*i
x4 = 78.0162175641465
x5 = -95.8185756187215 + 2.0743905954131e-12*i
x6 = 25.6563400043166
x7 = -58.1194639744525 - 4.87648410934991e-10*i
x8 = -79.0634151153431
x9 = 67.5442423570946 - 2.07613852397706e-8*i
x10 = -12.0427718387609
x11 = 69.6386371545737
x12 = 42.4115006780177 + 9.97123898639632e-10*i
x13 = 82.2050077689329
x14 = -24.60914245312
x15 = -14.1371668101748 - 6.73027598357791e-10*i
x16 = -53.9306738866248
x17 = -97.9129710368819
x18 = -18.3259571459405
x19 = 90.5825881785057
x20 = -1.57079648482414 + 1.28078825127311e-9*i
x21 = 84.2994028713261
x22 = -70.6858343771339 - 1.34760457834021e-7*i
x23 = 61.2610570621899 - 2.13875588913498e-7*i
x24 = 63.3554518473942
x25 = -7.85398146463811 - 5.26914615074372e-10*i
x26 = -56.025068989018
x27 = -83.2522056338029 + 2.86061549753028e-8*i
x28 = 80.1106131462877 + 4.26129915488116e-9*i
x29 = 38.2227106186758
x30 = 29.8451303535299 - 8.98980975296124e-10*i
x31 = 31.9395253114962
x32 = -30.8923277602996
x33 = 92.6769829895713 + 1.59518598729896e-8*i
x34 = 40.317105721069
x35 = -64.4026491128574 - 1.32809793846754e-8*i
x36 = 13.0899693899575
x37 = -20.4203519557306 - 1.54461099129452e-8*i
x38 = -62.3082542961976
x39 = -41.3643032722656
x40 = -74.8746249105567
x41 = 73.8274275167114 - 1.17096011317883e-9*i
x42 = -47.6474885794452
x43 = -9.94837673636768
x44 = 86.3937978413209 + 7.60069527246801e-10*i
x45 = -91.6297857297023
x46 = 54.9778711175888 + 1.9127516030938e-7*i
x47 = 46.6002910282486
x48 = -3.66519142918809
x49 = 75.9218224617533
x50 = 96.8657734856853
x51 = 34.0339204138894
x52 = -5.75958653158129
x53 = -100.007366139275
x54 = 98.9601682642763 + 1.63619662175812e-7*i
x55 = 36.1283157514137 + 2.09990693241767e-8*i
x56 = 4.71238867688039 + 2.1420566504936e-8*i
x57 = -76.9690203192575 + 3.14040934640957e-7*i
x58 = 0.0
x59 = -51.836278658197 - 7.64905682876905e-11*i
x60 = -49.7418836818384
x61 = -45.5530936472307 + 1.61745469880125e-9*i
x62 = -35.081117965086
x63 = -89.5353908092206 + 2.01436256738409e-9*i
x64 = -26.7035372299132 - 1.56718735495445e-7*i
x65 = 52.8834763354282
x66 = 2.61799387799149
x67 = 19.3731546971371
x68 = -39.269908478721 + 2.47674138629608e-8*i
x69 = 8.90117918517108
x70 = 17.2787599165259 - 1.82767500228721e-7*i
x71 = -93.7241808320955
x72 = 48.6946858329834 + 1.85005682131332e-8*i
x73 = -85.3466004225227
x74 = -68.5914396033772
x74 = -68.5914396033772