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5sinxcosx-15cosx=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
5*sin(x)*cos(x) - 15*cos(x) = 0
$$5 \sin{\left(x \right)} \cos{\left(x \right)} - 15 \cos{\left(x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -pi 
x1 = ----
      2
$$x_{1} = - \frac{\pi}{2}$$ 
     pi
x2 = --
     2
$$x_{2} = \frac{\pi}{2}$$ 
         /    /          ___\\         /    /          ___\\
         |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||
x3 = 2*re|atan|- - ---------|| + 2*I*im|atan|- - ---------||
         \    \3       3    //         \    \3       3    //
$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)}$$ 
         /    /          ___\\         /    /          ___\\
         |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||
x4 = 2*re|atan|- + ---------|| + 2*I*im|atan|- + ---------||
         \    \3       3    //         \    \3       3    //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)}$$ 
x4 = 2*re(atan(1/3 + 2*sqrt(2)*i/3)) + 2*i*im(atan(1/3 + 2*sqrt(2)*i/3))
Suma y producto de raíces [src] 
suma
                /    /          ___\\         /    /          ___\\       /    /          ___\\         /    /          ___\\
  pi   pi       |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||       |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||
- -- + -- + 2*re|atan|- - ---------|| + 2*I*im|atan|- - ---------|| + 2*re|atan|- + ---------|| + 2*I*im|atan|- + ---------||
  2    2        \    \3       3    //         \    \3       3    //       \    \3       3    //         \    \3       3    //
$$\left(\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)}\right)$$ 
=
    /    /          ___\\       /    /          ___\\         /    /          ___\\         /    /          ___\\
    |    |1   2*I*\/ 2 ||       |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||
2*re|atan|- - ---------|| + 2*re|atan|- + ---------|| + 2*I*im|atan|- - ---------|| + 2*I*im|atan|- + ---------||
    \    \3       3    //       \    \3       3    //         \    \3       3    //         \    \3       3    //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)}$$ 
producto
        /    /    /          ___\\         /    /          ___\\\ /    /    /          ___\\         /    /          ___\\\
-pi  pi |    |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 ||| |    |    |1   2*I*\/ 2 ||         |    |1   2*I*\/ 2 |||
----*--*|2*re|atan|- - ---------|| + 2*I*im|atan|- - ---------|||*|2*re|atan|- + ---------|| + 2*I*im|atan|- + ---------|||
 2   2  \    \    \3       3    //         \    \3       3    /// \    \    \3       3    //         \    \3       3    ///
$$- \frac{\pi}{2} \frac{\pi}{2} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)}\right)$$ 
=
     /    /    /          ___\\     /    /          ___\\\ /    /    /          ___\\     /    /          ___\\\
   2 |    |    |1   2*I*\/ 2 ||     |    |1   2*I*\/ 2 ||| |    |    |1   2*I*\/ 2 ||     |    |1   2*I*\/ 2 |||
-pi *|I*im|atan|- - ---------|| + re|atan|- - ---------|||*|I*im|atan|- + ---------|| + re|atan|- + ---------|||
     \    \    \3       3    //     \    \3       3    /// \    \    \3       3    //     \    \3       3    ///
$$- \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{2 \sqrt{2} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{2 \sqrt{2} i}{3} \right)}\right)}\right)$$ 
-pi^2*(i*im(atan(1/3 - 2*i*sqrt(2)/3)) + re(atan(1/3 - 2*i*sqrt(2)/3)))*(i*im(atan(1/3 + 2*i*sqrt(2)/3)) + re(atan(1/3 + 2*i*sqrt(2)/3)))
Respuesta numérica [src] 
x1 = 48.6946861306418
x2 = 54.9778714378214
x3 = 306.305283725005
x4 = -98.9601685880785
x5 = 67.5442420521806
x6 = 76.9690200129499
x7 = 36.1283155162826
x8 = 58.1194640914112
x9 = 14.1371669411541
x10 = -29.845130209103
x11 = 61.261056745001
x12 = -36.1283155162826
x13 = -4.71238898038469
x14 = -39.2699081698724
x15 = 1.5707963267949
x16 = -14.1371669411541
x17 = -64.4026493985908
x18 = -67.5442420521806
x19 = 92.6769832808989
x20 = -51.8362787842316
x21 = -86.3937979737193
x22 = 42.4115008234622
x23 = -17.2787595947439
x24 = -45.553093477052
x25 = 102.101761241668
x26 = -89.5353906273091
x27 = -1.5707963267949
x28 = 39.2699081698724
x29 = 23.5619449019235
x30 = 479.092879672443
x31 = 7.85398163397448
x32 = -58.1194640914112
x33 = -61.261056745001
x34 = -73.8274273593601
x35 = 73.8274273593601
x36 = 29.845130209103
x37 = 4.71238898038469
x38 = 86.3937979737193
x39 = 64.4026493985908
x40 = 89.5353906273091
x41 = -20.4203522483337
x42 = -26.7035375555132
x43 = 98.9601685880785
x44 = 51.8362787842316
x45 = 83.2522053201295
x46 = -48.6946861306418
x47 = -54.9778714378214
x48 = 70.6858347057703
x49 = -95.8185759344887
x50 = 26.7035375555132
x51 = 80.1106126665397
x52 = -23.5619449019235
x53 = -7.85398163397448
x54 = -83.2522053201295
x55 = -76.9690200129499
x56 = -42.4115008234622
x57 = -32.9867228626928
x58 = 17.2787595947439
x59 = 32.9867228626928
x60 = 20.4203522483337
x61 = -70.6858347057703
x62 = -10.9955742875643
x63 = -92.6769832808989
x64 = 45.553093477052
x65 = 10.9955742875643
x66 = -80.1106126665397
x67 = 95.8185759344887
x67 = 95.8185759344887
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