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cos^3(x)=sin^3(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   3         3   
cos (x) = sin (x)
$$\cos^{3}{\left(x \right)} = \sin^{3}{\left(x \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
         /    /        ___\\       /    /        ___\\       /    /        ___\\       /    /        ___\\
pi       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
-- + - re|atan|- - -------|| - I*im|atan|- - -------|| + - re|atan|- + -------|| - I*im|atan|- + -------||
4        \    \2      2   //       \    \2      2   //       \    \2      2   //       \    \2      2   //
$$\left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) + \left(\frac{\pi}{4} + \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right)$$
=
    /    /        ___\\     /    /        ___\\            /    /        ___\\       /    /        ___\\
    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||   pi       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
- re|atan|- + -------|| - re|atan|- - -------|| + -- - I*im|atan|- + -------|| - I*im|atan|- - -------||
    \    \2      2   //     \    \2      2   //   4        \    \2      2   //       \    \2      2   //
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + \frac{\pi}{4} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$
producto
   /    /    /        ___\\       /    /        ___\\\ /    /    /        ___\\       /    /        ___\\\
pi |    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 |||
--*|- re|atan|- - -------|| - I*im|atan|- - -------|||*|- re|atan|- + -------|| - I*im|atan|- + -------|||
4  \    \    \2      2   //       \    \2      2   /// \    \    \2      2   //       \    \2      2   ///
$$\frac{\pi}{4} \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$
=
   /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
   |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
pi*|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
   \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
------------------------------------------------------------------------------------------------------
                                                  4                                                   
$$\frac{\pi \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)}{4}$$
pi*(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)))/4
Respuesta rápida [src]
     pi
x1 = --
     4 
$$x_{1} = \frac{\pi}{4}$$
         /    /        ___\\       /    /        ___\\
         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
x2 = - re|atan|- - -------|| - I*im|atan|- - -------||
         \    \2      2   //       \    \2      2   //
$$x_{2} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$
         /    /        ___\\       /    /        ___\\
         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
x3 = - re|atan|- + -------|| - I*im|atan|- + -------||
         \    \2      2   //       \    \2      2   //
$$x_{3} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$
x3 = -re(atan(1/2 + sqrt(3)*i/2)) - i*im(atan(1/2 + sqrt(3)*i/2))
Respuesta numérica [src]
x1 = -115.453530019425
x2 = -46.3384916404494
x3 = -90.3207887907066
x4 = -36.9137136796801
x5 = -77.7544181763474
x6 = 3.92699081698724
x7 = -18.0641577581413
x8 = -84.037603483527
x9 = 54.1924732744239
x10 = 126.449104306989
x11 = 19.6349540849362
x12 = -633.816317861741
x13 = -756.338431351743
x14 = 38.484510006475
x15 = -11.7809724509617
x16 = 69.9004365423729
x17 = 88.7499924639117
x18 = -62.0464549083984
x19 = -2.35619449019234
x20 = 107.59954838545
x21 = 32.2013246992954
x22 = -49.4800842940392
x23 = -5.49778714378214
x24 = 57.3340659280137
x25 = 10.2101761241668
x26 = 60.4756585816035
x27 = -71.4712328691678
x28 = -27.4889357189107
x29 = 76.1836218495525
x30 = 82.4668071567321
x31 = -80.8960108299372
x32 = 63.6172512351933
x33 = -24.3473430653209
x34 = -335.36501577071
x35 = -14450.5408083497
x36 = 16.4933614313464
x37 = -55.7632696012188
x38 = -93.4623814442964
x39 = 85.6083998103219
x40 = -40.0553063332699
x41 = 29.0597320457056
x42 = 41.6261026600648
x43 = 25.9181393921158
x44 = 98.174770424681
x45 = -33.7721210260903
x46 = 47.9092879672443
x47 = -68.329640215578
x48 = 91.8915851175014
x49 = -99.7455667514759
x50 = 51.0508806208341
x50 = 51.0508806208341