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Expresiones idénticas
- (cos(x))^(tres)+(cos(y))^(tres)= tres *cos(x)*cos(y)
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- (cos(x))(3)+(cos(y))(3)=3*cos(x)*cos(y)
- cosx3+cosy3=3*cosx*cosy
- (cos(x))^(3)+(cos(y))^(3)=3cos(x)cos(y)
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- cosx3+cosy3=3cosxcosy
- cosx^3+cosy^3=3cosxcosy
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Expresiones semejantes
- (cos(x))^(3)-(cos(y))^(3)=3*cos(x)*cos(y)
- (cosx)^(3)+(cos(y))^(3)=3*cosx*cos(y)
-
Expresiones con funciones
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
(cos(x))^(3)+(cos(y))^(3)=3*cos(x)*cos(y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 3 cos (x) + cos (y) = 3*cos(x)*cos(y)
$$\cos^{3}{\left(x \right)} + \cos^{3}{\left(y \right)} = 3 \cos{\left(x \right)} \cos{\left(y \right)}$$
Gráfica
Respuesta rápida
[src]
/ // _________________ \ \\ / // _________________ \ \\
| || / ___ / ___\| || | || / ___ / ___\| ||
| || / 27 27*I*\/ 3 | 1 I*\/ 3 || || | || / 27 27*I*\/ 3 | 1 I*\/ 3 || ||
| || 3 / -- + ---------- *|- - - -------|| || | || 3 / -- + ---------- *|- - - -------|| ||
| || 3 \/ 2 2 \ 2 2 /| || | || 3 \/ 2 2 \ 2 2 /| ||
x1 = - re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
| || _________________ 3 | || | || _________________ 3 | ||
| || / ___\ / ___ | || | || / ___\ / ___ | ||
| || | 1 I*\/ 3 | / 27 27*I*\/ 3 | || | || | 1 I*\/ 3 | / 27 27*I*\/ 3 | ||
| || |- - - -------|*3 / -- + ---------- | || | || |- - - -------|*3 / -- + ---------- | ||
\ \\ \ 2 2 / \/ 2 2 / // \ \\ \ 2 2 / \/ 2 2 / //
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi$$
/ // _________________ \ \\ / // _________________ \ \\
| || / ___ / ___\| || | || / ___ / ___\| ||
| || / 27 27*I*\/ 3 | 1 I*\/ 3 || || | || / 27 27*I*\/ 3 | 1 I*\/ 3 || ||
| || 3 / -- + ---------- *|- - + -------|| || | || 3 / -- + ---------- *|- - + -------|| ||
| || 3 \/ 2 2 \ 2 2 /| || | || 3 \/ 2 2 \ 2 2 /| ||
x2 = - re|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + 2*pi - I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
| || _________________ 3 | || | || _________________ 3 | ||
| || / ___\ / ___ | || | || / ___\ / ___ | ||
| || | 1 I*\/ 3 | / 27 27*I*\/ 3 | || | || | 1 I*\/ 3 | / 27 27*I*\/ 3 | ||
| || |- - + -------|*3 / -- + ---------- | || | || |- - + -------|*3 / -- + ---------- | ||
\ \\ \ 2 2 / \/ 2 2 / // \ \\ \ 2 2 / \/ 2 2 / //
$$x_{2} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi$$
/ // _________________\ \\ / // _________________\ \\
| || / ___ | || | || / ___ | ||
| || / 27 27*I*\/ 3 | || | || / 27 27*I*\/ 3 | ||
| || 3 / -- + ---------- | || | || 3 / -- + ---------- | ||
| || 3 \/ 2 2 | || | || 3 \/ 2 2 | ||
x3 = - re|acos||- ---------------------- - ----------------------|*cos(y)|| + 2*pi - I*im|acos||- ---------------------- - ----------------------|*cos(y)||
| || _________________ 3 | || | || _________________ 3 | ||
| || / ___ | || | || / ___ | ||
| || / 27 27*I*\/ 3 | || | || / 27 27*I*\/ 3 | ||
| || 3 / -- + ---------- | || | || 3 / -- + ---------- | ||
\ \\ \/ 2 2 / // \ \\ \/ 2 2 / //
$$x_{3} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + 2 \pi$$
/ // _________________ \ \\ / // _________________ \ \\
| || / ___ / ___\| || | || / ___ / ___\| ||
| || / 27 27*I*\/ 3 | 1 I*\/ 3 || || | || / 27 27*I*\/ 3 | 1 I*\/ 3 || ||
| || 3 / -- + ---------- *|- - - -------|| || | || 3 / -- + ---------- *|- - - -------|| ||
| || 3 \/ 2 2 \ 2 2 /| || | || 3 \/ 2 2 \ 2 2 /| ||
x4 = I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
| || _________________ 3 | || | || _________________ 3 | ||
| || / ___\ / ___ | || | || / ___\ / ___ | ||
| || | 1 I*\/ 3 | / 27 27*I*\/ 3 | || | || | 1 I*\/ 3 | / 27 27*I*\/ 3 | ||
| || |- - - -------|*3 / -- + ---------- | || | || |- - - -------|*3 / -- + ---------- | ||
\ \\ \ 2 2 / \/ 2 2 / // \ \\ \ 2 2 / \/ 2 2 / //
$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3}\right) \cos{\left(y \right)} \right)}\right)}$$
/ // _________________ \ \\ / // _________________ \ \\
| || / ___ / ___\| || | || / ___ / ___\| ||
| || / 27 27*I*\/ 3 | 1 I*\/ 3 || || | || / 27 27*I*\/ 3 | 1 I*\/ 3 || ||
| || 3 / -- + ---------- *|- - + -------|| || | || 3 / -- + ---------- *|- - + -------|| ||
| || 3 \/ 2 2 \ 2 2 /| || | || 3 \/ 2 2 \ 2 2 /| ||
x5 = I*im|acos||- -------------------------------------- - --------------------------------------|*cos(y)|| + re|acos||- -------------------------------------- - --------------------------------------|*cos(y)||
| || _________________ 3 | || | || _________________ 3 | ||
| || / ___\ / ___ | || | || / ___\ / ___ | ||
| || | 1 I*\/ 3 | / 27 27*I*\/ 3 | || | || | 1 I*\/ 3 | / 27 27*I*\/ 3 | ||
| || |- - + -------|*3 / -- + ---------- | || | || |- - + -------|*3 / -- + ---------- | ||
\ \\ \ 2 2 / \/ 2 2 / // \ \\ \ 2 2 / \/ 2 2 / //
$$x_{5} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)}$$
/ // _________________\ \\ / // _________________\ \\
| || / ___ | || | || / ___ | ||
| || / 27 27*I*\/ 3 | || | || / 27 27*I*\/ 3 | ||
| || 3 / -- + ---------- | || | || 3 / -- + ---------- | ||
| || 3 \/ 2 2 | || | || 3 \/ 2 2 | ||
x6 = I*im|acos||- ---------------------- - ----------------------|*cos(y)|| + re|acos||- ---------------------- - ----------------------|*cos(y)||
| || _________________ 3 | || | || _________________ 3 | ||
| || / ___ | || | || / ___ | ||
| || / 27 27*I*\/ 3 | || | || / 27 27*I*\/ 3 | ||
| || 3 / -- + ---------- | || | || 3 / -- + ---------- | ||
\ \\ \/ 2 2 / // \ \\ \/ 2 2 / //
$$x_{6} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(- \frac{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}{3} - \frac{3}{\sqrt[3]{\frac{27}{2} + \frac{27 \sqrt{3} i}{2}}}\right) \cos{\left(y \right)} \right)}\right)}$$
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
/ // _________________ \ \\ / // _________________ \ \\ / // _________________ \ \\ / // _________________ \ \\ / // _________________\ \\ / // _________________\ \\ / // _________________ \ \\ / // _________________ \ \\ / // _________________ \ \\ / // _________________ \ \\ / // _________________\ \\ / // _________________\ \\
| || / ___ / ___\| || | || / ___ / ___\| || | || / ___ / ___\| || | || / ___ / ___\| || | || / ___ | || | || / ___ | || | || / ___ / ___\| || | || / ___ / ___\| || | || / ___ / ___\| || | || / ___ / ___\| || | || / ___ | || | || / ___ | ||
| || / 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 | 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 | ||
| || 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 / //
$$\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
$$6 \pi$$
producto
/ / // _________________ \ \\ / // _________________ \ \\\ / / // _________________ \ \\ / // _________________ \ \\\ / / // _________________\ \\ / // _________________\ \\\ / / // _________________ \ \\ / // _________________ \ \\\ / / // _________________ \ \\ / // _________________ \ \\\ / / // _________________\ \\ / // _________________\ \\\ | | || / ___ / ___\| || | || / ___ / ___\| ||| | | || / ___ / ___\| || | || / ___ / ___\| ||| | | || / ___ | || | || / ___ | ||| | | || / ___ / ___\| || | || / ___ / ___\| ||| | | || / ___ / ___\| || | || / ___ / ___\| ||| | | || / ___ | || | || / ___ | ||| | | || / 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 | 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 | ||| | | || 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 / ///
$$\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////
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \sin{\left(\frac{\pi}{18} \right)} \cos{\left(y \right)} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- 2 \cos{\left(\frac{\pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} - 2 \pi\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \cos{\left(\frac{2 \pi}{9} \right)} \cos{\left(y \right)} \right)}\right)} - 2 \pi\right)$$
-(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))))