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sinx*cosx=-cbrt(2)/4 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                 3 ___ 
                -\/ 2  
sin(x)*cos(x) = -------
                   4   
$$\sin{\left(x \right)} \cos{\left(x \right)} = \frac{\left(-1\right) \sqrt[3]{2}}{4}$$
Gráfica
Suma y producto de raíces [src]
suma
        /     _________________________________                           \         /            _________________________________                    \         /            _________________________________                    \         /                                _________________________________\
        |    /                               2                            |         |           /                               2                     |         |           /                               2                     |         |                               /                               2 |
        |   /      /          ______________\        ______________       |         |          /      /          ______________\        ______________|         |          /      /          ______________\        ______________|         |          ______________      /      /          ______________\  |
        |  /       | 2/3     /        3 ___ |       /        3 ___     2/3|         | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |         | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |         | 2/3     /        3 ___      /       | 2/3     /        3 ___ |  |
- 2*atan\\/    1 + \2    - \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2   - 2   / + 2*atan\2    + \/    1 + \2    - \/  -1 + 2*\/ 2  /   - \/  -1 + 2*\/ 2  / + 2*atan\2    + \/    1 + \2    + \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2  / + 2*atan\2    + \/  -1 + 2*\/ 2   - \/    1 + \2    + \/  -1 + 2*\/ 2  /  /
$$2 \operatorname{atan}{\left(- \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} + \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} \right)} + \left(\left(- 2 \operatorname{atan}{\left(- 2^{\frac{2}{3}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + \sqrt{-1 + 2 \sqrt[3]{2}} \right)} + 2 \operatorname{atan}{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + 2^{\frac{2}{3}} \right)}\right) + 2 \operatorname{atan}{\left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} + \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} \right)}\right)$$
=
        /     _________________________________                           \         /            _________________________________                    \         /            _________________________________                    \         /                                _________________________________\
        |    /                               2                            |         |           /                               2                     |         |           /                               2                     |         |                               /                               2 |
        |   /      /          ______________\        ______________       |         |          /      /          ______________\        ______________|         |          /      /          ______________\        ______________|         |          ______________      /      /          ______________\  |
        |  /       | 2/3     /        3 ___ |       /        3 ___     2/3|         | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |         | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |         | 2/3     /        3 ___      /       | 2/3     /        3 ___ |  |
- 2*atan\\/    1 + \2    - \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2   - 2   / + 2*atan\2    + \/    1 + \2    + \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2  / + 2*atan\2    + \/    1 + \2    - \/  -1 + 2*\/ 2  /   - \/  -1 + 2*\/ 2  / + 2*atan\2    + \/  -1 + 2*\/ 2   - \/    1 + \2    + \/  -1 + 2*\/ 2  /  /
$$- 2 \operatorname{atan}{\left(- 2^{\frac{2}{3}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + \sqrt{-1 + 2 \sqrt[3]{2}} \right)} + 2 \operatorname{atan}{\left(- \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} + \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} \right)} + 2 \operatorname{atan}{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + 2^{\frac{2}{3}} \right)} + 2 \operatorname{atan}{\left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} + \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} \right)}$$
producto
       /     _________________________________                           \       /            _________________________________                    \       /            _________________________________                    \       /                                _________________________________\
       |    /                               2                            |       |           /                               2                     |       |           /                               2                     |       |                               /                               2 |
       |   /      /          ______________\        ______________       |       |          /      /          ______________\        ______________|       |          /      /          ______________\        ______________|       |          ______________      /      /          ______________\  |
       |  /       | 2/3     /        3 ___ |       /        3 ___     2/3|       | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |       | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |       | 2/3     /        3 ___      /       | 2/3     /        3 ___ |  |
-2*atan\\/    1 + \2    - \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2   - 2   /*2*atan\2    + \/    1 + \2    - \/  -1 + 2*\/ 2  /   - \/  -1 + 2*\/ 2  /*2*atan\2    + \/    1 + \2    + \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2  /*2*atan\2    + \/  -1 + 2*\/ 2   - \/    1 + \2    + \/  -1 + 2*\/ 2  /  /
$$- 2 \operatorname{atan}{\left(- 2^{\frac{2}{3}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + \sqrt{-1 + 2 \sqrt[3]{2}} \right)} 2 \operatorname{atan}{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + 2^{\frac{2}{3}} \right)} 2 \operatorname{atan}{\left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} + \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} \right)} 2 \operatorname{atan}{\left(- \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} + \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} \right)}$$
=
        /            _________________________________                    \     /            _________________________________                    \     /                                _________________________________\     /     _________________________________                           \
        |           /                               2                     |     |           /                               2                     |     |                               /                               2 |     |    /                               2                            |
        |          /      /          ______________\        ______________|     |          /      /          ______________\        ______________|     |          ______________      /      /          ______________\  |     |   /      /          ______________\        ______________       |
        | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |     | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |     | 2/3     /        3 ___      /       | 2/3     /        3 ___ |  |     |  /       | 2/3     /        3 ___ |       /        3 ___     2/3|
-16*atan\2    + \/    1 + \2    + \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2  /*atan\2    + \/    1 + \2    - \/  -1 + 2*\/ 2  /   - \/  -1 + 2*\/ 2  /*atan\2    + \/  -1 + 2*\/ 2   - \/    1 + \2    + \/  -1 + 2*\/ 2  /  /*atan\\/    1 + \2    - \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2   - 2   /
$$- 16 \operatorname{atan}{\left(- 2^{\frac{2}{3}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + \sqrt{-1 + 2 \sqrt[3]{2}} \right)} \operatorname{atan}{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + 2^{\frac{2}{3}} \right)} \operatorname{atan}{\left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} + \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} \right)} \operatorname{atan}{\left(- \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} + \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} \right)}$$
-16*atan(2^(2/3) + sqrt(1 + (2^(2/3) + sqrt(-1 + 2*2^(1/3)))^2) + sqrt(-1 + 2*2^(1/3)))*atan(2^(2/3) + sqrt(1 + (2^(2/3) - sqrt(-1 + 2*2^(1/3)))^2) - sqrt(-1 + 2*2^(1/3)))*atan(2^(2/3) + sqrt(-1 + 2*2^(1/3)) - sqrt(1 + (2^(2/3) + sqrt(-1 + 2*2^(1/3)))^2))*atan(sqrt(1 + (2^(2/3) - sqrt(-1 + 2*2^(1/3)))^2) + sqrt(-1 + 2*2^(1/3)) - 2^(2/3))
Respuesta rápida [src]
            /     _________________________________                           \
            |    /                               2                            |
            |   /      /          ______________\        ______________       |
            |  /       | 2/3     /        3 ___ |       /        3 ___     2/3|
x1 = -2*atan\\/    1 + \2    - \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2   - 2   /
$$x_{1} = - 2 \operatorname{atan}{\left(- 2^{\frac{2}{3}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + \sqrt{-1 + 2 \sqrt[3]{2}} \right)}$$
           /            _________________________________                    \
           |           /                               2                     |
           |          /      /          ______________\        ______________|
           | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |
x2 = 2*atan\2    + \/    1 + \2    - \/  -1 + 2*\/ 2  /   - \/  -1 + 2*\/ 2  /
$$x_{2} = 2 \operatorname{atan}{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + \sqrt{\left(- \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2} + 1} + 2^{\frac{2}{3}} \right)}$$
           /            _________________________________                    \
           |           /                               2                     |
           |          /      /          ______________\        ______________|
           | 2/3     /       | 2/3     /        3 ___ |       /        3 ___ |
x3 = 2*atan\2    + \/    1 + \2    + \/  -1 + 2*\/ 2  /   + \/  -1 + 2*\/ 2  /
$$x_{3} = 2 \operatorname{atan}{\left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} + \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} \right)}$$
           /                                _________________________________\
           |                               /                               2 |
           |          ______________      /      /          ______________\  |
           | 2/3     /        3 ___      /       | 2/3     /        3 ___ |  |
x4 = 2*atan\2    + \/  -1 + 2*\/ 2   - \/    1 + \2    + \/  -1 + 2*\/ 2  /  /
$$x_{4} = 2 \operatorname{atan}{\left(- \sqrt{1 + \left(\sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}}\right)^{2}} + \sqrt{-1 + 2 \sqrt[3]{2}} + 2^{\frac{2}{3}} \right)}$$
x4 = 2*atan(-sqrt(1 + (sqrt(-1 + 2*2^(1/3)) + 2^(2/3))^2) + sqrt(-1 + 2*2^(1/3)) + 2^(2/3))
Respuesta numérica [src]
x1 = -23.2211937110827
x2 = 8.19473282481519
x3 = -42.0707496326215
x4 = -94.5885307985345
x5 = 90.7654357632633
x6 = 27.0442887463539
x7 = -0.340751190840707
x8 = -63.1726042626366
x9 = -75.7389748769957
x10 = 37.3583606522368
x11 = 87.6238431096735
x12 = 100.190213724033
x13 = -53.7478263018672
x14 = 12.2256194235185
x15 = -35.7875643254419
x16 = -45.2123422862113
x17 = -97.7301234521243
x18 = -9.76552915161009
x19 = -29.5043790182623
x20 = 18.5088047306981
x21 = -57.7787129005705
x22 = 5.94243411633888
x23 = 21.6503973842878
x24 = 30.1858813999437
x25 = -86.0530467828786
x26 = -16.0487144587897
x27 = 20.7611034391744
x28 = 14.4779181319948
x29 = -44.3230483410978
x30 = 67.8849932430213
x31 = 58.4602152822519
x32 = 65.632694534545
x33 = 62.4911018809552
x34 = -31.7566777267386
x35 = -485.035313788782
x36 = 49.924731266596
x37 = -50.6062336482774
x38 = 1.9115475176356
x39 = 74.1681785502008
x40 = -79.769861475699
x41 = 23.9026960927642
x42 = 93.9070284168531
x43 = -13.7964157503134
x44 = 27.9335826914674
x45 = -72.597382223406
x46 = -95.477824743648
x47 = 59.3495092273654
x48 = 42.7522520143029
x49 = -66.3141969162264
x50 = 71.9158798417245
x51 = 96.1593271253294
x52 = 78.1990651489041
x53 = -82.0221601841753
x54 = -1.23004513595419
x55 = -67.2034908613398
x56 = 56.2079165737756
x57 = -3.4823438444305
x58 = -7.51323044313378
x59 = 86.73454916456
x60 = -60.0310116090468
x61 = 64.7434005894315
x62 = -51.4955275933909
x63 = 40.4999533058266
x64 = 46.7831386130062
x65 = 81.3406578024939
x66 = -88.3053454913549
x67 = -73.4866761685194
x68 = -25.4734924195591
x69 = 34.216767998647
x70 = -20.0796010574929
x71 = 52.1770299750723
x72 = -64.06189820775
x73 = 84.4822504560837
x74 = 80.4513638573804
x75 = 89.8761418181498
x76 = -38.0398630339182
x77 = 36.4690667071233
x78 = -22.3318997659693
x79 = 45.8938446678927
x80 = 43.6415459594164
x81 = 15.3672120771083
x82 = -6.62393649802029
x83 = -89.1946394364684
x84 = -28.6150850731488
x84 = -28.6150850731488