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sinx*(cosx*sinx-1)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(x)*(cos(x)*sin(x) - 1) = 0
$$\left(\sin{\left(x \right)} \cos{\left(x \right)} - 1\right) \sin{\left(x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
    /    /                         _____________\\         /    /                         _____________\\         /    /                       _____________\\         /    /                       _____________\\         /    /                       _____________\\         /    /                       _____________\\         /    /             _____________          \\         /    /             _____________          \\
    |    |          ___     ___   /         ___ ||         |    |          ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||         |    |      ___   /         ___        ___||         |    |      ___   /         ___        ___||
    |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||
2*re|atan|- - + ------- + ----------------------|| + 2*I*im|atan|- - + ------- + ----------------------|| + - 2*re|atan|- + ------- - ----------------------|| - 2*I*im|atan|- + ------- - ----------------------|| + - 2*re|atan|- + ------- + ----------------------|| - 2*I*im|atan|- + ------- + ----------------------|| + - 2*re|atan|- + ---------------------- - -------|| - 2*I*im|atan|- + ---------------------- - -------||
    \    \  2      2                2           //         \    \  2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2             2                 2   //         \    \2             2                 2   //
$$\left(\left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)}\right)$$
=
      /    /                       _____________\\       /    /                       _____________\\       /    /             _____________          \\       /    /                         _____________\\         /    /                       _____________\\         /    /                       _____________\\         /    /             _____________          \\         /    /                         _____________\\
      |    |        ___     ___   /         ___ ||       |    |        ___     ___   /         ___ ||       |    |      ___   /         ___        ___||       |    |          ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||         |    |      ___   /         ___        ___||         |    |          ___     ___   /         ___ ||
      |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||       |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||       |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||
- 2*re|atan|- + ------- + ----------------------|| - 2*re|atan|- + ------- - ----------------------|| - 2*re|atan|- + ---------------------- - -------|| + 2*re|atan|- - + ------- + ----------------------|| - 2*I*im|atan|- + ------- + ----------------------|| - 2*I*im|atan|- + ------- - ----------------------|| - 2*I*im|atan|- + ---------------------- - -------|| + 2*I*im|atan|- - + ------- + ----------------------||
      \    \2      2                2           //       \    \2      2                2           //       \    \2             2                 2   //       \    \  2      2                2           //         \    \2      2                2           //         \    \2      2                2           //         \    \2             2                 2   //         \    \  2      2                2           //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$
producto
  /    /    /                         _____________\\         /    /                         _____________\\\ /      /    /                       _____________\\         /    /                       _____________\\\ /      /    /                       _____________\\         /    /                       _____________\\\ /      /    /             _____________          \\         /    /             _____________          \\\
  |    |    |          ___     ___   /         ___ ||         |    |          ___     ___   /         ___ ||| |      |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||| |      |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||| |      |    |      ___   /         ___        ___||         |    |      ___   /         ___        ___|||
  |    |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||| |      |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||| |      |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||| |      |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 |||
0*|2*re|atan|- - + ------- + ----------------------|| + 2*I*im|atan|- - + ------- + ----------------------|||*|- 2*re|atan|- + ------- - ----------------------|| - 2*I*im|atan|- + ------- - ----------------------|||*|- 2*re|atan|- + ------- + ----------------------|| - 2*I*im|atan|- + ------- + ----------------------|||*|- 2*re|atan|- + ---------------------- - -------|| - 2*I*im|atan|- + ---------------------- - -------|||
  \    \    \  2      2                2           //         \    \  2      2                2           /// \      \    \2      2                2           //         \    \2      2                2           /// \      \    \2      2                2           //         \    \2      2                2           /// \      \    \2             2                 2   //         \    \2             2                 2   ///
$$0 \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
         /    /                         _____________\\         /    /                         _____________\\
         |    |          ___     ___   /         ___ ||         |    |          ___     ___   /         ___ ||
         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||         |    |  1   I*\/ 3    \/ 2 *\/  1 - I*\/ 3  ||
x2 = 2*re|atan|- - + ------- + ----------------------|| + 2*I*im|atan|- - + ------- + ----------------------||
         \    \  2      2                2           //         \    \  2      2                2           //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$
           /    /                       _____________\\         /    /                       _____________\\
           |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||
           |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||
x3 = - 2*re|atan|- + ------- - ----------------------|| - 2*I*im|atan|- + ------- - ----------------------||
           \    \2      2                2           //         \    \2      2                2           //
$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$
           /    /                       _____________\\         /    /                       _____________\\
           |    |        ___     ___   /         ___ ||         |    |        ___     ___   /         ___ ||
           |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||         |    |1   I*\/ 3    \/ 2 *\/  1 + I*\/ 3  ||
x4 = - 2*re|atan|- + ------- + ----------------------|| - 2*I*im|atan|- + ------- + ----------------------||
           \    \2      2                2           //         \    \2      2                2           //
$$x_{4} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{3} i}}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$
           /    /             _____________          \\         /    /             _____________          \\
           |    |      ___   /         ___        ___||         |    |      ___   /         ___        ___||
           |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||         |    |1   \/ 2 *\/  1 - I*\/ 3     I*\/ 3 ||
x5 = - 2*re|atan|- + ---------------------- - -------|| - 2*I*im|atan|- + ---------------------- - -------||
           \    \2             2                 2   //         \    \2             2                 2   //
$$x_{5} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{3} i}}{2} \right)}\right)}$$
x5 = -2*re(atan(1/2 - sqrt(3)*i/2 + sqrt(2)*sqrt(1 - sqrt(3)*i)/2)) - 2*i*im(atan(1/2 - sqrt(3)*i/2 + sqrt(2)*sqrt(1 - sqrt(3)*i)/2))
Respuesta numérica [src]
x1 = 72.2566310325652
x2 = -59.6902604182061
x3 = 3.14159265358979
x4 = -43.9822971502571
x5 = 81.6814089933346
x6 = -100.530964914873
x7 = 28.2743338823081
x8 = 65.9734457253857
x9 = -31.4159265358979
x10 = -9.42477796076938
x11 = 40.8407044966673
x12 = 56.5486677646163
x13 = -56.5486677646163
x14 = 12.5663706143592
x15 = 43.9822971502571
x16 = 100.530964914873
x17 = -3.14159265358979
x18 = -15.707963267949
x19 = 59.6902604182061
x20 = 6.28318530717959
x21 = 9.42477796076938
x22 = -53.4070751110265
x23 = -47.1238898038469
x24 = -87.9645943005142
x25 = 69.1150383789755
x26 = 21.9911485751286
x27 = 87.9645943005142
x28 = 18.8495559215388
x29 = -84.8230016469244
x30 = -72.2566310325652
x31 = 25.1327412287183
x32 = 37.6991118430775
x33 = -25.1327412287183
x34 = 0.0
x35 = 50.2654824574367
x36 = -6.28318530717959
x37 = -65.9734457253857
x38 = -21.9911485751286
x39 = -62.8318530717959
x40 = 75.398223686155
x41 = 84.8230016469244
x42 = 53.4070751110265
x43 = 34.5575191894877
x44 = -28.2743338823081
x45 = 15.707963267949
x46 = -91.106186954104
x47 = 47.1238898038469
x48 = 97.3893722612836
x49 = -69.1150383789755
x50 = 94.2477796076938
x51 = -18.8495559215388
x52 = -50.2654824574367
x53 = -37.6991118430775
x54 = -81.6814089933346
x55 = 62.8318530717959
x56 = 78.5398163397448
x57 = 31.4159265358979
x58 = -78.5398163397448
x59 = -40.8407044966673
x60 = -97.3893722612836
x61 = -75.398223686155
x62 = 91.106186954104
x63 = -12.5663706143592
x64 = -94.2477796076938
x65 = -34.5575191894877
x65 = -34.5575191894877