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sin(x)-2sin(x)cos(x)+4cos(x)-2=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
sin(x) - 2*sin(x)*cos(x) + 4*cos(x) - 2 = 0
$$\left(\left(\sin{\left(x \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) + 4 \cos{\left(x \right)}\right) - 2 = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                /    /        ___\\         /    /        ___\\       /    /        ___\\         /    /        ___\\
  pi   pi       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
- -- + -- + 2*re|atan|- - -------|| + 2*I*im|atan|- - -------|| + 2*re|atan|- + -------|| + 2*I*im|atan|- + -------||
  3    3        \    \2      2   //         \    \2      2   //       \    \2      2   //         \    \2      2   //
$$\left(\left(- \frac{\pi}{3} + \frac{\pi}{3}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$ 
=
    /    /        ___\\       /    /        ___\\         /    /        ___\\         /    /        ___\\
    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
2*re|atan|- + -------|| + 2*re|atan|- - -------|| + 2*I*im|atan|- + -------|| + 2*I*im|atan|- - -------||
    \    \2      2   //       \    \2      2   //         \    \2      2   //         \    \2      2   //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$ 
producto
        /    /    /        ___\\         /    /        ___\\\ /    /    /        ___\\         /    /        ___\\\
-pi  pi |    |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||         |    |1   I*\/ 3 |||
----*--*|2*re|atan|- - -------|| + 2*I*im|atan|- - -------|||*|2*re|atan|- + -------|| + 2*I*im|atan|- + -------|||
 3   3  \    \    \2      2   //         \    \2      2   /// \    \    \2      2   //         \    \2      2   ///
$$- \frac{\pi}{3} \frac{\pi}{3} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$ 
=
       /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
     2 |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
-4*pi *|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
       \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
----------------------------------------------------------------------------------------------------------
                                                    9
$$- \frac{4 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)}{9}$$ 
-4*pi^2*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))/9
Respuesta rápida [src] 
     -pi 
x1 = ----
      3
$$x_{1} = - \frac{\pi}{3}$$ 
     pi
x2 = --
     3
$$x_{2} = \frac{\pi}{3}$$ 
         /    /        ___\\         /    /        ___\\
         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
x3 = 2*re|atan|- - -------|| + 2*I*im|atan|- - -------||
         \    \2      2   //         \    \2      2   //
$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$ 
         /    /        ___\\         /    /        ___\\
         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
x4 = 2*re|atan|- + -------|| + 2*I*im|atan|- + -------||
         \    \2      2   //         \    \2      2   //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$ 
x4 = 2*re(atan(1/2 + sqrt(3)*i/2)) + 2*i*im(atan(1/2 + sqrt(3)*i/2))
Respuesta numérica [src] 
x1 = 36.6519142918809
x2 = -24.0855436775217
x3 = 11.5191730631626
x4 = -32.4631240870945
x5 = 32.4631240870945
x6 = 26.1799387799149
x7 = 49.2182849062401
x8 = -7.33038285837618
x9 = 99.4837673636768
x10 = 17.8023583703422
x11 = -95.2949771588904
x12 = -42.9350995990605
x13 = -68.0678408277789
x14 = 19.8967534727354
x15 = 4786.74000651965
x16 = 45.0294947014537
x17 = -26.1799387799149
x18 = -86.9173967493176
x19 = 80.634211442138
x20 = 57.5958653158129
x21 = 7.33038285837618
x22 = 24.0855436775217
x23 = 95.2949771588904
x24 = -19.8967534727354
x25 = -13.6135681655558
x26 = -30.3687289847013
x27 = 38.7463093942741
x28 = 82.7286065445312
x29 = 5.23598775598299
x30 = -45.0294947014537
x31 = 1.0471975511966
x32 = -1.0471975511966
x33 = -93.2005820564972
x34 = 4286.17957704767
x35 = -5.23598775598299
x36 = -11.5191730631626
x37 = -74.3510261349584
x38 = -57.5958653158129
x39 = 42.9350995990605
x40 = 86.9173967493176
x41 = 76.4454212373516
x42 = -80.634211442138
x43 = 55.5014702134197
x44 = -89.0117918517108
x45 = -38.7463093942741
x46 = -17.8023583703422
x47 = 89.0117918517108
x48 = -51.3126800086333
x49 = -55.5014702134197
x50 = 63.8790506229925
x51 = 68.0678408277789
x52 = -76.4454212373516
x53 = 101.57816246607
x54 = 51.3126800086333
x55 = -99.4837673636768
x56 = -49.2182849062401
x57 = -36.6519142918809
x58 = -63.8790506229925
x59 = 61.7846555205993
x60 = 13.6135681655558
x61 = 74.3510261349584
x62 = -70.162235930172
x63 = 93.2005820564972
x64 = 70.162235930172
x65 = -82.7286065445312
x66 = -61.7846555205993
x67 = 30.3687289847013
x67 = 30.3687289847013
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