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sin3x×cosx-cos3x×sinx=√3/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                                      ___
                                    \/ 3 
sin(3*x)*cos(x) - cos(3*x)*sin(x) = -----
                                      2
$$- \sin{\left(x \right)} \cos{\left(3 x \right)} + \sin{\left(3 x \right)} \cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
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 /|
6    3       3       \  2                /      6       \  2                /
$$\left(\left(\frac{\pi}{6} + \frac{\pi}{3}\right) + \left(- \frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)\right) + \left(- \frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$ 
=
          /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 /||
6  3  \   3       \  2                // \   6       \  2                //
$$\frac{\pi}{6} \frac{\pi}{3} \left(- \frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right) \left(- \frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$ 
=
    4
5*pi 
-----
 162
$$\frac{5 \pi^{4}}{162}$$ 
5*pi^4/162
Respuesta rápida [src] 
     pi
x1 = --
     6
$$x_{1} = \frac{\pi}{6}$$ 
     pi
x2 = --
     3
$$x_{2} = \frac{\pi}{3}$$ 
       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 = 292.691715559449
x2 = -81.1578102177363
x3 = -87.4409955249159
x4 = 79.5870138909414
x5 = -83.7758040957278
x6 = -65.4498469497874
x7 = 101.054563690472
x8 = -36.6519142918809
x9 = 50.789081233035
x10 = 73.3038285837618
x11 = 63.8790506229925
x12 = -24.0855436775217
x13 = -59.1666616426078
x14 = -2.0943951023932
x15 = -15.1843644923507
x16 = 44.5058959258554
x17 = 95.2949771588904
x18 = 41.8879020478639
x19 = -5.75958653158129
x20 = -58.6430628670095
x21 = 70.162235930172
x22 = -39.7935069454707
x23 = -96.342174710087
x24 = 35.081117965086
x25 = -80.634211442138
x26 = 97.9129710368819
x27 = 26.1799387799149
x28 = -21.4675497995303
x29 = -18.3259571459405
x30 = 48.1710873550435
x31 = 7.33038285837618
x32 = 57.5958653158129
x33 = 66.497044500984
x34 = -68.0678408277789
x35 = 0.523598775598299
x36 = 6.80678408277789
x37 = 29.3215314335047
x38 = -93.7241808320955
x39 = 75.9218224617533
x40 = -74.3510261349584
x41 = 85.870199198121
x42 = 35.6047167406843
x43 = -34.0339204138894
x44 = 92.1533845053006
x45 = 72.7802298081635
x46 = 82.2050077689329
x47 = 9.94837673636768
x48 = 60.2138591938044
x49 = 31.9395253114962
x50 = -49.7418836818384
x51 = 25.6563400043166
x52 = -52.3598775598299
x53 = 38.2227106186758
x54 = 19.8967534727354
x55 = -90.0589894029074
x56 = 53.9306738866248
x57 = 51.3126800086333
x58 = -61.7846555205993
x59 = -37.1755130674792
x60 = -8.37758040957278
x61 = 28.7979326579064
x62 = 4.18879020478639
x63 = 38.7463093942741
x64 = 57.0722665402146
x65 = -46.0766922526503
x66 = -17.8023583703422
x67 = -56.025068989018
x68 = 94.7713783832921
x69 = 16.2315620435473
x70 = -78.0162175641465
x71 = -14.6607657167524
x72 = 60.7374579694027
x73 = -12.0427718387609
x74 = 79.0634151153431
x75 = 13.6135681655558
x76 = -100.007366139275
x77 = -30.3687289847013
x78 = -71.733032256967
x79 = -27.7507351067098
x80 = 22.5147473507269
x81 = 23.0383461263252
x82 = 314.682864134578
x83 = -43.4586983746588
x84 = 88.4881930761125
x84 = 88.4881930761125
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