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(cos(x))^(3)+(cos(y))^(3)=3*cos(x)*cos(y) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   3         3                     
cos (x) + cos (y) = 3*cos(x)*cos(y)
cos⁡3(x)+cos⁡3(y)=3cos⁡(x)cos⁡(y)\cos^{3}{\left(x \right)} + \cos^{3}{\left(y \right)} = 3 \cos{\left(x \right)} \cos{\left(y \right)}
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Respuesta rápida [src] 
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x1 = - re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
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         \    \\  \  2      2   / \/    2        2                                               /       //              \    \\  \  2      2   / \/    2        2                                               /       //
x1=−re⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))−iim⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))+2πx_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi 
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x2 = - re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
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x2=−re⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))−iim⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))+2πx_{2} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi 
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x3 = - re|acos||- ---------------------- - ----------------------|*cos(y)|| + 2*pi - I*im|acos||- ---------------------- - ----------------------|*cos(y)||
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x3=−re⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))−iim⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))+2πx_{3} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi 
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x4 = I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
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x4=re⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))+iim⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} 
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x5 = I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
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x5=re⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))+iim⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))x_{5} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} 
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x6 = I*im|acos||- ---------------------- - ----------------------|*cos(y)|| + re|acos||- ---------------------- - ----------------------|*cos(y)||
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x6=re⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))+iim⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))x_{6} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} 
x6 = re(acos((-(27/2 + 27*sqrt(3)*i/2)^(1/3)/3 - 3/(27/2 + 27*sqrt(3)*i/2)^(1/3))*cos(y))) + i*im(acos((-(27/2 + 27*sqrt(3)*i/2)^(1/3)/3 - 3/(27/2 + 27*sqrt(3)*i/2)^(1/3))*cos(y)))
Suma y producto de raíces [src] 
suma
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- re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + - re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + - re|acos||- ---------------------- - ----------------------|*cos(y)|| + 2*pi - I*im|acos||- ---------------------- - ----------------------|*cos(y)|| + I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + I*im|acos||- ---------------------- - ----------------------|*cos(y)|| + re|acos||- ---------------------- - ----------------------|*cos(y)||
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    |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||              |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||       |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||              |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||       |    ||     /  27   27*I*\/ 3                           |       ||              |    ||     /  27   27*I*\/ 3                           |       ||       |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||     |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||       |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||     |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||       |    ||     /  27   27*I*\/ 3                           |       ||     |    ||     /  27   27*I*\/ 3                           |       ||
    |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||              |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||       |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||              |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||       |    ||  3 /   -- + ----------                          |       ||              |    ||  3 /   -- + ----------                          |       ||       |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||     |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||       |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||     |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||       |    ||  3 /   -- + ----------                          |       ||     |    ||  3 /   -- + ----------                          |       ||
    \    \\  \  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      2   / \/    2        2                                               /       //       \    \\  \  2      2   / \/    2        2                                               /       //     \    \\  \  2      2   / \/    2        2                                               /       //       \    \\  \/    2        2                               /       //     \    \\  \/    2        2                               /       //
(((((−re⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))−iim⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))+2π)+(−re⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))−iim⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))+2π))+(−re⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))−iim⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))+2π))+(re⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))+iim⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))))+(re⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))+iim⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))))+(re⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))+iim⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y))))\left(\left(\left(\left(\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi\right)\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)}\right) 
=
6*pi
6π6 \pi 
producto
/    /    //                                                _________________                \       \\              /    //                                                _________________                \       \\\ /    /    //                                                _________________                \       \\              /    //                                                _________________                \       \\\ /    /    //                                _________________\       \\              /    //                                _________________\       \\\ /    /    //                                                _________________                \       \\     /    //                                                _________________                \       \\\ /    /    //                                                _________________                \       \\     /    //                                                _________________                \       \\\ /    /    //                                _________________\       \\     /    //                                _________________\       \\\
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|    |    ||                                           3 /   -- + ---------- *|- - - -------||       ||              |    ||                                           3 /   -- + ---------- *|- - - -------||       ||| |    |    ||                                           3 /   -- + ---------- *|- - + -------||       ||              |    ||                                           3 /   -- + ---------- *|- - + -------||       ||| |    |    ||                           3 /   -- + ---------- |       ||              |    ||                           3 /   -- + ---------- |       ||| |    |    ||                                           3 /   -- + ---------- *|- - - -------||       ||     |    ||                                           3 /   -- + ---------- *|- - - -------||       ||| |    |    ||                                           3 /   -- + ---------- *|- - + -------||       ||     |    ||                                           3 /   -- + ---------- *|- - + -------||       ||| |    |    ||                           3 /   -- + ---------- |       ||     |    ||                           3 /   -- + ---------- |       |||
|    |    ||                    3                      \/    2        2       \  2      2   /|       ||              |    ||                    3                      \/    2        2       \  2      2   /|       ||| |    |    ||                    3                      \/    2        2       \  2      2   /|       ||              |    ||                    3                      \/    2        2       \  2      2   /|       ||| |    |    ||            3              \/    2        2      |       ||              |    ||            3              \/    2        2      |       ||| |    |    ||                    3                      \/    2        2       \  2      2   /|       ||     |    ||                    3                      \/    2        2       \  2      2   /|       ||| |    |    ||                    3                      \/    2        2       \  2      2   /|       ||     |    ||                    3                      \/    2        2       \  2      2   /|       ||| |    |    ||            3              \/    2        2      |       ||     |    ||            3              \/    2        2      |       |||
|- re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|||*|- re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|||*|- re|acos||- ---------------------- - ----------------------|*cos(y)|| + 2*pi - I*im|acos||- ---------------------- - ----------------------|*cos(y)|||*|I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|||*|I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|||*|I*im|acos||- ---------------------- - ----------------------|*cos(y)|| + re|acos||- ---------------------- - ----------------------|*cos(y)|||
|    |    ||                       _________________                     3                   |       ||              |    ||                       _________________                     3                   |       ||| |    |    ||                       _________________                     3                   |       ||              |    ||                       _________________                     3                   |       ||| |    |    ||       _________________             3           |       ||              |    ||       _________________             3           |       ||| |    |    ||                       _________________                     3                   |       ||     |    ||                       _________________                     3                   |       ||| |    |    ||                       _________________                     3                   |       ||     |    ||                       _________________                     3                   |       ||| |    |    ||       _________________             3           |       ||     |    ||       _________________             3           |       |||
|    |    ||  /          ___\     /             ___                                          |       ||              |    ||  /          ___\     /             ___                                          |       ||| |    |    ||  /          ___\     /             ___                                          |       ||              |    ||  /          ___\     /             ___                                          |       ||| |    |    ||      /             ___                          |       ||              |    ||      /             ___                          |       ||| |    |    ||  /          ___\     /             ___                                          |       ||     |    ||  /          ___\     /             ___                                          |       ||| |    |    ||  /          ___\     /             ___                                          |       ||     |    ||  /          ___\     /             ___                                          |       ||| |    |    ||      /             ___                          |       ||     |    ||      /             ___                          |       |||
|    |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||              |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||| |    |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||              |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||| |    |    ||     /  27   27*I*\/ 3                           |       ||              |    ||     /  27   27*I*\/ 3                           |       ||| |    |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||     |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||| |    |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||     |    ||  |  1   I*\/ 3 |    /  27   27*I*\/ 3                                           |       ||| |    |    ||     /  27   27*I*\/ 3                           |       ||     |    ||     /  27   27*I*\/ 3                           |       |||
|    |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||              |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||| |    |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||              |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||| |    |    ||  3 /   -- + ----------                          |       ||              |    ||  3 /   -- + ----------                          |       ||| |    |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||     |    ||  |- - - -------|*3 /   -- + ----------                                          |       ||| |    |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||     |    ||  |- - + -------|*3 /   -- + ----------                                          |       ||| |    |    ||  3 /   -- + ----------                          |       ||     |    ||  3 /   -- + ----------                          |       |||
\    \    \\  \  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      2   / \/    2        2                                               /       /// \    \    \\  \  2      2   / \/    2        2                                               /       //     \    \\  \  2      2   / \/    2        2                                               /       /// \    \    \\  \/    2        2                               /       //     \    \\  \/    2        2                               /       ///
(−re⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))−iim⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))+2π)(−re⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))−iim⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))+2π)(−re⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))−iim⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))+2π)(re⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y)))+iim⁡(acos⁡((−3(−12−3i2)272+273i23−(−12−3i2)272+273i233)cos⁡(y))))(re⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y)))+iim⁡(acos⁡((−(−12+3i2)272+273i233−3(−12+3i2)272+273i23)cos⁡(y))))(re⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y)))+iim⁡(acos⁡((−272+273i233−3272+273i23)cos⁡(y))))\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)}\right) 
=
 /    /    /             /pi\\\     /    /             /pi\\\\ /    /    /            /2*pi\\\     /    /            /2*pi\\\\ /    /    /            /pi\\\     /    /            /pi\\\\ /            /    /             /pi\\\     /    /             /pi\\\\ /            /    /            /2*pi\\\     /    /            /2*pi\\\\ /            /    /            /pi\\\     /    /            /pi\\\\
-|I*im|acos|-2*cos(y)*cos|--||| + re|acos|-2*cos(y)*cos|--||||*|I*im|acos|2*cos(y)*cos|----||| + re|acos|2*cos(y)*cos|----||||*|I*im|acos|2*cos(y)*sin|--||| + re|acos|2*cos(y)*sin|--||||*|-2*pi + I*im|acos|-2*cos(y)*cos|--||| + re|acos|-2*cos(y)*cos|--||||*|-2*pi + I*im|acos|2*cos(y)*cos|----||| + re|acos|2*cos(y)*cos|----||||*|-2*pi + I*im|acos|2*cos(y)*sin|--||| + re|acos|2*cos(y)*sin|--||||
 \    \    \             \9 ///     \    \             \9 //// \    \    \            \ 9  ///     \    \            \ 9  //// \    \    \            \18///     \    \            \18//// \            \    \             \9 ///     \    \             \9 //// \            \    \            \ 9  ///     \    \            \ 9  //// \            \    \            \18///     \    \            \18////
−(re⁡(acos⁡(2sin⁡(π18)cos⁡(y)))+iim⁡(acos⁡(2sin⁡(π18)cos⁡(y))))(re⁡(acos⁡(−2cos⁡(π9)cos⁡(y)))+iim⁡(acos⁡(−2cos⁡(π9)cos⁡(y))))(re⁡(acos⁡(2cos⁡(2π9)cos⁡(y)))+iim⁡(acos⁡(2cos⁡(2π9)cos⁡(y))))(re⁡(acos⁡(2sin⁡(π18)cos⁡(y)))+iim⁡(acos⁡(2sin⁡(π18)cos⁡(y)))−2π)(re⁡(acos⁡(−2cos⁡(π9)cos⁡(y)))+iim⁡(acos⁡(−2cos⁡(π9)cos⁡(y)))−2π)(re⁡(acos⁡(2cos⁡(2π9)cos⁡(y)))+iim⁡(acos⁡(2cos⁡(2π9)cos⁡(y)))−2π)- \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} - 2 \pi\right) 
-(i*im(acos(-2*cos(y)*cos(pi/9))) + re(acos(-2*cos(y)*cos(pi/9))))*(i*im(acos(2*cos(y)*cos(2*pi/9))) + re(acos(2*cos(y)*cos(2*pi/9))))*(i*im(acos(2*cos(y)*sin(pi/18))) + re(acos(2*cos(y)*sin(pi/18))))*(-2*pi + i*im(acos(-2*cos(y)*cos(pi/9))) + re(acos(-2*cos(y)*cos(pi/9))))*(-2*pi + i*im(acos(2*cos(y)*cos(2*pi/9))) + re(acos(2*cos(y)*cos(2*pi/9))))*(-2*pi + i*im(acos(2*cos(y)*sin(pi/18))) + re(acos(2*cos(y)*sin(pi/18))))
    © Sr Examen – Калькулятор