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sin5xcos3x-cos5xsin3x=-(sqrt(3)/2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                                           ___ 
                                        -\/ 3  
sin(5*x)*cos(3*x) - cos(5*x)*sin(3*x) = -------
                                           2
$$- \sin{\left(3 x \right)} \cos{\left(5 x \right)} + \sin{\left(5 x \right)} \cos{\left(3 x \right)} = - \frac{\sqrt{3}}{2}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  pi   pi   2*pi     /log(2)      /  ___\\   5*pi     /log(2)      /  ___\\
- -- - -- + ---- + I*|------ - log\\/ 2 /| + ---- + I*|------ - log\\/ 2 /|
  3    6     3       \  2                /    6       \  2                /
$$\left(\left(- \frac{\pi}{3} - \frac{\pi}{6}\right) + \left(\frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)\right) + \left(\frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$ 
=
         /log(2)      /  ___\\
pi + 2*I*|------ - log\\/ 2 /|
         \  2                /
$$\pi + 2 i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$ 
producto
-pi  -pi  /2*pi     /log(2)      /  ___\\\ /5*pi     /log(2)      /  ___\\\
----*----*|---- + I*|------ - log\\/ 2 /||*|---- + I*|------ - log\\/ 2 /||
 3    6   \ 3       \  2                // \ 6       \  2                //
$$- \frac{\pi}{3} \left(- \frac{\pi}{6}\right) \left(\frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right) \left(\frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$ 
=
    4
5*pi 
-----
 162
$$\frac{5 \pi^{4}}{162}$$ 
5*pi^4/162
Respuesta rápida [src] 
     -pi 
x1 = ----
      3
$$x_{1} = - \frac{\pi}{3}$$ 
     -pi 
x2 = ----
      6
$$x_{2} = - \frac{\pi}{6}$$ 
     2*pi     /log(2)      /  ___\\
x3 = ---- + I*|------ - log\\/ 2 /|
      3       \  2                /
$$x_{3} = \frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$ 
     5*pi     /log(2)      /  ___\\
x4 = ---- + I*|------ - log\\/ 2 /|
      6       \  2                /
$$x_{4} = \frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$ 
x4 = 5*pi/6 + i*(-log(sqrt(2)) + log(2)/2)
Respuesta numérica [src] 
x1 = -29.3215314335047
x2 = -25.6563400043166
x3 = -60.2138591938044
x4 = -73.3038285837618
x5 = -16.7551608191456
x6 = 84.2994028713261
x7 = 80.634211442138
x8 = 96.342174710087
x9 = 24.0855436775217
x10 = 42.9350995990605
x11 = -35.6047167406843
x12 = 18.3259571459405
x13 = -91.6297857297023
x14 = 5.75958653158129
x15 = -242.426233102012
x16 = 49.7418836818384
x17 = -57.5958653158129
x18 = -4.18879020478639
x19 = 8.90117918517108
x20 = 65.4498469497874
x21 = 27.7507351067098
x22 = 15.1843644923507
x23 = 71.2094334813686
x24 = -31.9395253114962
x25 = 36.6519142918809
x26 = -97.9129710368819
x27 = 86.9173967493176
x28 = 52.3598775598299
x29 = -82.2050077689329
x30 = 93.7241808320955
x31 = -9.94837673636768
x32 = 64.9262481741891
x33 = -51.3126800086333
x34 = -67.0206432765823
x35 = -41.8879020478639
x36 = -261.799387799149
x37 = -94.7713783832921
x38 = 46.0766922526503
x39 = 87.4409955249159
x40 = -23.0383461263252
x41 = 78.0162175641465
x42 = 100.007366139275
x43 = -45.0294947014537
x44 = -7.33038285837618
x45 = -13.6135681655558
x46 = -75.9218224617533
x47 = 20.943951023932
x48 = -53.9306738866248
x49 = -72.7802298081635
x50 = 124.616508592395
x51 = -19.8967534727354
x52 = -16.2315620435473
x53 = -85.870199198121
x54 = -63.8790506229925
x55 = -44.5058959258554
x56 = 30.3687289847013
x57 = 68.5914396033772
x58 = -6.80678408277789
x59 = 14.6607657167524
x60 = 74.3510261349584
x61 = -88.4881930761125
x62 = -95.2949771588904
x63 = -60.7374579694027
x64 = 8.37758040957278
x65 = 12.0427718387609
x66 = -0.523598775598299
x67 = 62.3082542961976
x68 = 37.1755130674792
x69 = -28.7979326579064
x70 = 71.733032256967
x71 = 90.0589894029074
x72 = -79.5870138909414
x73 = -89.0117918517108
x74 = -69.6386371545737
x75 = -22.5147473507269
x76 = 40.317105721069
x77 = 58.6430628670095
x78 = -1.0471975511966
x79 = -47.6474885794452
x80 = 56.025068989018
x81 = -3.66519142918809
x82 = 34.0339204138894
x83 = -66.497044500984
x84 = -50.789081233035
x85 = 43.4586983746588
x86 = 68.0678408277789
x87 = 2.0943951023932
x88 = 21.4675497995303
x89 = -38.2227106186758
x89 = -38.2227106186758
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