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- La ecuación:
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Ecuación -x+7=0
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Ecuación x+(x/4)=-5
- Ecuación z^4-81=0
-
Ecuación z^3=8
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
- Integral de d{x}:
- cos(4x)
- Derivada de:
-
cos(4x)
- Gráfico de la función y =:
-
cos(4x)
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Expresiones idénticas
- Sin(5x)=cos(4x)
- Sin(5x) es igual a coseno de (4x)
- Sin5x=cos4x
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Expresiones semejantes
- 2*cos(4*x)-2*cos(x)^(2)=3*cos(2*x)
- 3+5sin2x=cos4x
- cos(4*x)*cos(x)-cos(5*x)=0
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Expresiones con funciones
- Coseno cos
- cos(3*x)-cos(7x)=0
- cos(x)+cos(2*x)+cos(3*x)=3
- cos(x)=cos(4)
- cos^2(x)=0.1*e^x
- cos(x)*sin(x)=-1/2
Sin(5x)=cos(4x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Suma y producto de raíces
[src]
suma
/ / /pi\\\ / /2*pi\ /pi\ \
| | 2*cos|--||| | cos|----| cos|--| |
| ___ | 1 /2*pi\ \9 /|| | 1 \ 9 / 1 \9 / |
/ ________________________________________________________________________________________________________________________________\ |\/ 3 *|-2 + ------- + 4*cos|----| - ---------|| / _____________________________________________________________________________________________________________________________________________\ |- - + --------- - --------- + ---------|
| / /2*pi\ 2/2*pi\ /pi\ /pi\ /2*pi\ 2/pi\ /pi\ /2*pi\ | | | /pi\ \ 9 / /pi\ || / /pi\\ / /5*pi\\ / 2/pi\\ | / /2*pi\ 2/2*pi\ /pi\ /2*pi\ /pi\ 2/pi\ /pi\ /2*pi\ | | 4 2 /pi\ /pi\|
| / cos|----| cos |----| cos|--| cos|--| cos|----| cos |--| cos|--|*cos|----| | | | sin|--| sin|--| || / _____________________\ |cos|--|| |sin|----|| / _________________________\ / ________________________________________\ |1 - 2*cos |--|| | / cos|----| cos |----| cos|--| cos|----| cos|--| cos |--| cos|--|*cos|----| | | 8*sin|--| 4*sin|--||
5*pi pi pi 17*pi | / 13 \ 9 / 1 \ 9 / 1 \9 / \9 / \ 9 / \9 / \9 / \ 9 / | | \ \18/ \18/ /| | / 2/pi\ 2/pi\ | | \9 /| | \ 18 /| | / 2/2*pi\ 2/5*pi\ | | / 2/pi\ 2/pi\ 4/pi\ | | \18/| | / 1 2/2*pi\ \ 9 / \ 9 / 1 1 \9 / \ 9 / \9 / \9 / \9 / \ 9 / | | \18/ \18/|
- ---- + -- + -- + ----- + - I*log| / -- - --------- - ---------- + ---------- + ----------- - ----------- + --------- + --------- + ----------- - ----------------- | + atan|----------------------------------------------| + -pi - I*log| / cos |--| + sin |--| | + atan|-------| + pi - atan|---------| - I*log| / sin |----| + sin |----| | + - I*log| / 1 + sin |--| - 4*cos |--| + 4*cos |--| | + atan|--------------| + - I*log| / -- + sin |----| - --------- + ---------- + ---------- + ----------- - --------- - --------- - ----------- + ----------- + ----------------- | + atan|---------------------------------------|
6 18 2 18 | / 16 4 /pi\ 4 2/pi\ 2/pi\ /pi\ /pi\ 2/pi\ /pi\ | \ 12 / \\/ \9 / \9 / / | /pi\| | /2*pi\| \\/ \ 9 / \ 18 / / \\/ \9 / \18/ \18/ / | /pi\ | | / 16 \ 9 / 4 4 /pi\ 2/pi\ /pi\ /pi\ 2/pi\ 2/pi\ /pi\ | | /2*pi\ |
| / 16*sin|--| 64*sin |--| 16*sin |--| 8*sin|--| 8*sin|--| 16*sin |--| 4*sin|--| | |sin|--|| |sin|----|| | sin|--| | | / 16*sin|--| 64*sin |--| 8*sin|--| 8*sin|--| 16*sin |--| 16*sin |--| 4*sin|--| | | sin|----| |
\\/ \18/ \18/ \18/ \18/ \18/ \18/ \18/ / \ \9 // \ \ 9 // \ \9 / / \\/ \18/ \18/ \18/ \18/ \18/ \18/ \18/ / \ \ 9 / /
$$\left(\left(\operatorname{atan}{\left(\frac{1 - 2 \cos^{2}{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)} - i \log{\left(\sqrt{- 4 \cos^{2}{\left(\frac{\pi}{18} \right)} + \sin^{2}{\left(\frac{\pi}{9} \right)} + 1 + 4 \cos^{4}{\left(\frac{\pi}{18} \right)}} \right)}\right) + \left(\left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)}\right) + \left(\left(\operatorname{atan}{\left(\frac{\sqrt{3} \left(- \frac{2 \cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} - 2 + 4 \cos{\left(\frac{2 \pi}{9} \right)} + \frac{1}{\sin{\left(\frac{\pi}{18} \right)}}\right)}{12} \right)} - i \log{\left(\sqrt{- \frac{\cos{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}} - \frac{1}{16 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{\cos^{2}{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{64 \sin^{2}{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} + \frac{13}{16} + \frac{\cos^{2}{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}}} \right)}\right) + \left(\left(\left(- \frac{5 \pi}{6} + \frac{\pi}{18}\right) + \frac{\pi}{2}\right) + \frac{17 \pi}{18}\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{18} \right)}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{2 \pi}{9} \right)} + \sin^{2}{\left(\frac{5 \pi}{18} \right)}} \right)} + \pi\right)\right)\right) + \left(- i \log{\left(\sqrt{- \frac{\cos{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{\pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{16} + \frac{\cos^{2}{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{16 \sin{\left(\frac{\pi}{18} \right)}} + \sin^{2}{\left(\frac{2 \pi}{9} \right)} + \frac{1}{64 \sin^{2}{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}} + \frac{\cos^{2}{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}}} \right)} + \operatorname{atan}{\left(\frac{- \frac{1}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{1}{4} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)}\right)$$
=
/ /2*pi\ /pi\ \ / / /pi\\\
| cos|----| cos|--| | | | 2*cos|--|||
| 1 \ 9 / 1 \9 / | | ___ | 1 /2*pi\ \9 /||
/ ________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________\ |- - + --------- - --------- + ---------| |\/ 3 *|-2 + ------- + 4*cos|----| - ---------||
/ /5*pi\\ | / /2*pi\ 2/2*pi\ /pi\ /pi\ /2*pi\ 2/pi\ /pi\ /2*pi\ | | / /2*pi\ 2/2*pi\ /pi\ /2*pi\ /pi\ 2/pi\ /pi\ /2*pi\ | / 2/pi\\ / /pi\\ | 4 2 /pi\ /pi\| | | /pi\ \ 9 / /pi\ ||
|sin|----|| / _____________________\ / _________________________\ / ________________________________________\ | / cos|----| cos |----| cos|--| cos|--| cos|----| cos |--| cos|--|*cos|----| | | / cos|----| cos |----| cos|--| cos|----| cos|--| cos |--| cos|--|*cos|----| | |1 - 2*cos |--|| |cos|--|| | 8*sin|--| 4*sin|--|| | | sin|--| sin|--| ||
| \ 18 /| 2*pi | / 2/pi\ 2/pi\ | | / 2/2*pi\ 2/5*pi\ | | / 2/pi\ 2/pi\ 4/pi\ | | / 13 \ 9 / 1 \ 9 / 1 \9 / \9 / \ 9 / \9 / \9 / \ 9 / | | / 1 2/2*pi\ \ 9 / \ 9 / 1 1 \9 / \ 9 / \9 / \9 / \9 / \ 9 / | | \18/| | \9 /| | \18/ \18/| | \ \18/ \18/ /|
- atan|---------| + ---- - I*log| / cos |--| + sin |--| | - I*log| / sin |----| + sin |----| | - I*log| / 1 + sin |--| - 4*cos |--| + 4*cos |--| | - I*log| / -- - --------- - ---------- + ---------- + ----------- - ----------- + --------- + --------- + ----------- - ----------------- | - I*log| / -- + sin |----| - --------- + ---------- + ---------- + ----------- - --------- - --------- - ----------- + ----------- + ----------------- | + atan|--------------| + atan|-------| + atan|---------------------------------------| + atan|----------------------------------------------|
| /2*pi\| 3 \\/ \9 / \9 / / \\/ \ 9 / \ 18 / / \\/ \9 / \18/ \18/ / | / 16 4 /pi\ 4 2/pi\ 2/pi\ /pi\ /pi\ 2/pi\ /pi\ | | / 16 \ 9 / 4 4 /pi\ 2/pi\ /pi\ /pi\ 2/pi\ 2/pi\ /pi\ | | /pi\ | | /pi\| | /2*pi\ | \ 12 /
|sin|----|| | / 16*sin|--| 64*sin |--| 16*sin |--| 8*sin|--| 8*sin|--| 16*sin |--| 4*sin|--| | | / 16*sin|--| 64*sin |--| 8*sin|--| 8*sin|--| 16*sin |--| 16*sin |--| 4*sin|--| | | sin|--| | |sin|--|| | sin|----| |
\ \ 9 // \\/ \18/ \18/ \18/ \18/ \18/ \18/ \18/ / \\/ \18/ \18/ \18/ \18/ \18/ \18/ \18/ / \ \9 / / \ \9 // \ \ 9 / /
$$\operatorname{atan}{\left(\frac{1 - 2 \cos^{2}{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)} - \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{18} \right)}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \frac{2 \cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} - 2 + 4 \cos{\left(\frac{2 \pi}{9} \right)} + \frac{1}{\sin{\left(\frac{\pi}{18} \right)}}\right)}{12} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{2 \pi}{9} \right)} + \sin^{2}{\left(\frac{5 \pi}{18} \right)}} \right)} - i \log{\left(\sqrt{- 4 \cos^{2}{\left(\frac{\pi}{18} \right)} + \sin^{2}{\left(\frac{\pi}{9} \right)} + 1 + 4 \cos^{4}{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{- \frac{\cos{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}} - \frac{1}{16 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{\cos^{2}{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{64 \sin^{2}{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} + \frac{13}{16} + \frac{\cos^{2}{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}}} \right)} - i \log{\left(\sqrt{- \frac{\cos{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{\pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{16} + \frac{\cos^{2}{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{16 \sin{\left(\frac{\pi}{18} \right)}} + \sin^{2}{\left(\frac{2 \pi}{9} \right)} + \frac{1}{64 \sin^{2}{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}} + \frac{\cos^{2}{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}}} \right)} + \operatorname{atan}{\left(\frac{- \frac{1}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{1}{4} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)} + \frac{2 \pi}{3}$$
producto
/ / / /pi\\\\ / / /2*pi\ /pi\ \\
| | | 2*cos|--|||| | | cos|----| cos|--| ||
| | ___ | 1 /2*pi\ \9 /||| | | 1 \ 9 / 1 \9 / ||
| / ________________________________________________________________________________________________________________________________\ |\/ 3 *|-2 + ------- + 4*cos|----| - ---------||| | / _____________________________________________________________________________________________________________________________________________\ |- - + --------- - --------- + ---------||
| | / /2*pi\ 2/2*pi\ /pi\ /pi\ /2*pi\ 2/pi\ /pi\ /2*pi\ | | | /pi\ \ 9 / /pi\ ||| / / /pi\\\ / / /5*pi\\ \ / / 2/pi\\\ | | / /2*pi\ 2/2*pi\ /pi\ /2*pi\ /pi\ 2/pi\ /pi\ /2*pi\ | | 4 2 /pi\ /pi\||
| | / cos|----| cos |----| cos|--| cos|--| cos|----| cos |--| cos|--|*cos|----| | | | sin|--| sin|--| ||| | / _____________________\ |cos|--||| | |sin|----|| / _________________________\| | / ________________________________________\ |1 - 2*cos |--||| | | / cos|----| cos |----| cos|--| cos|----| cos|--| cos |--| cos|--|*cos|----| | | 8*sin|--| 4*sin|--|||
-5*pi pi pi 17*pi | | / 13 \ 9 / 1 \ 9 / 1 \9 / \9 / \ 9 / \9 / \9 / \ 9 / | | \ \18/ \18/ /|| | | / 2/pi\ 2/pi\ | | \9 /|| | | \ 18 /| | / 2/2*pi\ 2/5*pi\ || | | / 2/pi\ 2/pi\ 4/pi\ | | \18/|| | | / 1 2/2*pi\ \ 9 / \ 9 / 1 1 \9 / \ 9 / \9 / \9 / \9 / \ 9 / | | \18/ \18/||
-----*--*--*-----*|- I*log| / -- - --------- - ---------- + ---------- + ----------- - ----------- + --------- + --------- + ----------- - ----------------- | + atan|----------------------------------------------||*|-pi - I*log| / cos |--| + sin |--| | + atan|-------||*|pi - atan|---------| - I*log| / sin |----| + sin |----| ||*|- I*log| / 1 + sin |--| - 4*cos |--| + 4*cos |--| | + atan|--------------||*|- I*log| / -- + sin |----| - --------- + ---------- + ---------- + ----------- - --------- - --------- - ----------- + ----------- + ----------------- | + atan|---------------------------------------||
6 18 2 18 | | / 16 4 /pi\ 4 2/pi\ 2/pi\ /pi\ /pi\ 2/pi\ /pi\ | \ 12 /| | \\/ \9 / \9 / / | /pi\|| | | /2*pi\| \\/ \ 9 / \ 18 / /| | \\/ \9 / \18/ \18/ / | /pi\ || | | / 16 \ 9 / 4 4 /pi\ 2/pi\ /pi\ /pi\ 2/pi\ 2/pi\ /pi\ | | /2*pi\ ||
| | / 16*sin|--| 64*sin |--| 16*sin |--| 8*sin|--| 8*sin|--| 16*sin |--| 4*sin|--| | | | |sin|--||| | |sin|----|| | | | sin|--| || | | / 16*sin|--| 64*sin |--| 8*sin|--| 8*sin|--| 16*sin |--| 16*sin |--| 4*sin|--| | | sin|----| ||
\ \\/ \18/ \18/ \18/ \18/ \18/ \18/ \18/ / / \ \ \9 /// \ \ \ 9 // / \ \ \9 / // \ \\/ \18/ \18/ \18/ \18/ \18/ \18/ \18/ / \ \ 9 / //
$$\frac{17 \pi}{18} \frac{\pi}{2} \cdot - \frac{5 \pi}{6} \frac{\pi}{18} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \left(- \frac{2 \cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} - 2 + 4 \cos{\left(\frac{2 \pi}{9} \right)} + \frac{1}{\sin{\left(\frac{\pi}{18} \right)}}\right)}{12} \right)} - i \log{\left(\sqrt{- \frac{\cos{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}} - \frac{1}{16 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{\cos^{2}{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{64 \sin^{2}{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} + \frac{13}{16} + \frac{\cos^{2}{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}}} \right)}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{18} \right)}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{2 \pi}{9} \right)} + \sin^{2}{\left(\frac{5 \pi}{18} \right)}} \right)} + \pi\right) \left(\operatorname{atan}{\left(\frac{1 - 2 \cos^{2}{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)} - i \log{\left(\sqrt{- 4 \cos^{2}{\left(\frac{\pi}{18} \right)} + \sin^{2}{\left(\frac{\pi}{9} \right)} + 1 + 4 \cos^{4}{\left(\frac{\pi}{18} \right)}} \right)}\right) \left(- i \log{\left(\sqrt{- \frac{\cos{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{\pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{16} + \frac{\cos^{2}{\left(\frac{2 \pi}{9} \right)}}{4} + \frac{1}{16 \sin{\left(\frac{\pi}{18} \right)}} + \sin^{2}{\left(\frac{2 \pi}{9} \right)} + \frac{1}{64 \sin^{2}{\left(\frac{\pi}{18} \right)}} + \frac{\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}} + \frac{\cos^{2}{\left(\frac{\pi}{9} \right)}}{16 \sin^{2}{\left(\frac{\pi}{18} \right)}}} \right)} + \operatorname{atan}{\left(\frac{- \frac{1}{8 \sin{\left(\frac{\pi}{18} \right)}} - \frac{1}{4} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{4 \sin{\left(\frac{\pi}{18} \right)}}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)}\right)$$
=
/ / _______________________________________________________________________________________________\ \ / / _______________________________________________________________________________________________\ \
| | / /pi\ 2/pi\ 2/pi\ /pi\ 2/pi\ / 2/pi\ 4/pi\\ | / ___ / /2*pi\ /pi\ /pi\\\| | | / /pi\ 2/pi\ 2/pi\ / 4/pi\ 2/pi\\ 2/pi\ /pi\ | / /pi\ /2*pi\ /pi\\|
/ / ________________________________________\\ | | / 1 - 4*cos|--| + 4*cos |--| - 16*sin |--|*sin|--| + 4*sin |--|*|13 - 8*sin |--| + 16*sin |--|| | |\/ 3 *|- cos|----| + cos|--| + sin|--|||| | | / 1 - 4*cos|--| + 4*cos |--| + 4*sin |--|*|1 - 48*sin |--| + 56*sin |--|| + 16*sin |--|*sin|--| | |1 - cos|--| - cos|----| + sin|--|||
6 |7*pi | / 2/pi\ 2/pi\ 4/pi\ || | |\/ \9 / \9 / \9 / \18/ \18/ \ \9 / \9 // | | \ \ 9 / \9 / \18//|| | |\/ \9 / \9 / \18/ \ \9 / \9 // \9 / \18/ | | \9 / \ 9 / \18/||
-12155*pi *|---- + I*log| / 1 + sin |--| - 4*sin |--| + 4*sin |--| ||*|I*log|---------------------------------------------------------------------------------------------------| + atan|---------------------------------------||*|I*log|---------------------------------------------------------------------------------------------------| + atan|---------------------------------||
\ 18 \\/ \9 / \18/ \18/ // | | /pi\ | | /pi\ || | | /pi\ | | ___ /5*pi\ ||
| | 8*sin|--| | | 6*sin|--| || | | 8*sin|--| | | \/ 3 - 2*cos|----| ||
\ \ \18/ / \ \18/ // \ \ \18/ / \ \ 18 / //
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1259712
$$- \frac{12155 \pi^{6} \left(i \log{\left(\frac{\sqrt{- 4 \cos{\left(\frac{\pi}{9} \right)} - 16 \sin{\left(\frac{\pi}{18} \right)} \sin^{2}{\left(\frac{\pi}{9} \right)} + 1 + 4 \left(- 8 \sin^{2}{\left(\frac{\pi}{9} \right)} + 16 \sin^{4}{\left(\frac{\pi}{9} \right)} + 13\right) \sin^{2}{\left(\frac{\pi}{18} \right)} + 4 \cos^{2}{\left(\frac{\pi}{9} \right)}}}{8 \sin{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \cos{\left(\frac{2 \pi}{9} \right)} + \sin{\left(\frac{\pi}{18} \right)} + \cos{\left(\frac{\pi}{9} \right)}\right)}{6 \sin{\left(\frac{\pi}{18} \right)}} \right)}\right) \left(i \log{\left(\sqrt{- 4 \sin^{2}{\left(\frac{\pi}{18} \right)} + 4 \sin^{4}{\left(\frac{\pi}{18} \right)} + \sin^{2}{\left(\frac{\pi}{9} \right)} + 1} \right)} + \frac{7 \pi}{18}\right) \left(\operatorname{atan}{\left(\frac{- \cos{\left(\frac{\pi}{9} \right)} - \cos{\left(\frac{2 \pi}{9} \right)} + \sin{\left(\frac{\pi}{18} \right)} + 1}{- 2 \cos{\left(\frac{5 \pi}{18} \right)} + \sqrt{3}} \right)} + i \log{\left(\frac{\sqrt{- 4 \cos{\left(\frac{\pi}{9} \right)} + 16 \sin{\left(\frac{\pi}{18} \right)} \sin^{2}{\left(\frac{\pi}{9} \right)} + 4 \left(- 48 \sin^{4}{\left(\frac{\pi}{9} \right)} + 1 + 56 \sin^{2}{\left(\frac{\pi}{9} \right)}\right) \sin^{2}{\left(\frac{\pi}{18} \right)} + 1 + 4 \cos^{2}{\left(\frac{\pi}{9} \right)}}}{8 \sin{\left(\frac{\pi}{18} \right)}} \right)}\right)}{1259712}$$
-12155*pi^6*(7*pi/18 + i*log(sqrt(1 + sin(pi/9)^2 - 4*sin(pi/18)^2 + 4*sin(pi/18)^4)))*(i*log(sqrt(1 - 4*cos(pi/9) + 4*cos(pi/9)^2 - 16*sin(pi/9)^2*sin(pi/18) + 4*sin(pi/18)^2*(13 - 8*sin(pi/9)^2 + 16*sin(pi/9)^4))/(8*sin(pi/18))) + atan(sqrt(3)*(-cos(2*pi/9) + cos(pi/9) + sin(pi/18))/(6*sin(pi/18))))*(i*log(sqrt(1 - 4*cos(pi/9) + 4*cos(pi/9)^2 + 4*sin(pi/18)^2*(1 - 48*sin(pi/9)^4 + 56*sin(pi/9)^2) + 16*sin(pi/9)^2*sin(pi/18))/(8*sin(pi/18))) + atan((1 - cos(pi/9) - cos(2*pi/9) + sin(pi/18))/(sqrt(3) - 2*cos(5*pi/18))))/1259712
Respuesta numérica
[src]
x1 = 9.94837673636768
x2 = 78.3652834145454
x3 = -13.7881010907552
x4 = 83.9503370209273
x5 = -31.9395253114962
x6 = -25.6563400043166
x7 = -85.6956662729216
x8 = -45.9021593274509
x9 = 76.2708883121522
x10 = -36.1283154485727
x11 = -23.5619449540223
x12 = -43.8077642250577
x13 = 81.1578102177363
x14 = -36.12831520092
x15 = -20.0712863979348
x16 = -83.6012711705284
x17 = 28.0998009571087
x18 = 34.3829862642883
x19 = 39.9680398706701
x20 = -61.9591884457987
x21 = 30.1941960595019
x22 = -29.8451301093948
x23 = -11.693705988362
x24 = -27.7507351067098
x25 = 18.3259571459405
x26 = -87.7900613753148
x27 = 44.1568300754565
x28 = 16.2315620435473
x29 = 74.176493209759
x30 = 4.36332312998582
x31 = -15.8824961931484
x32 = 61.6101225953998
x33 = 86.0447321233204
x34 = -41.7133691226645
x35 = 95.8185759914842
x36 = 42.0624349730633
x37 = -4.01425727958696
x38 = 46.2512251778497
x39 = -47.9965544298441
x40 = 21.8166156499291
x41 = 62.3082542961976
x42 = -6.10865238198015
x43 = 1075.29735215371
x44 = -91.9788515801012
x45 = -53.5816080362259
x46 = -73.8274272827467
x47 = -73.1292956585624
x48 = -64.7517152489896
x49 = 37.873644768277
x50 = -9.59931088596881
x51 = 64.4026493358639
x52 = 53.9306738866248
x53 = -64.0535835481919
x54 = -1.91986217719376
x55 = -104.54522219446
x56 = -69.6386371545737
x57 = 26.0054058547155
x58 = -59.8647933434055
x59 = -75.9218224617533
x60 = 20.4203521882517
x61 = 60.2138591938044
x62 = -94.0732466824944
x63 = -99.6583002888762
x64 = 51.1381470834339
x65 = 0.174532925199433
x66 = 88.1391272257137
x67 = 23.2128790515246
x68 = -50.0909495322373
x69 = 72.0820981073658
x70 = 51.8362788484534
x71 = -78.0162175641465
x72 = 7.8539817013759
x73 = -55.6760031386191
x74 = -39.6189740202713
x75 = -34.0339204138894
x76 = 92.3279174305
x77 = -96.1676417848876
x78 = 97.9129710368819
x79 = -67.5442420868592
x80 = 94.4223125328932
x81 = -71.733032256967
x82 = -17.9768912955416
x83 = -89.884456477708
x84 = -66.1479786505851
x85 = 67.8933079025794
x86 = -22.165681500328
x87 = 7.85398191123749
x88 = 83.2522052880855
x89 = 69.9877030049726
x90 = 2.26892802759263
x91 = 23.9110107523223
x92 = -80.1106126008672
x93 = 90.2335223281068
x94 = 32.2885911618951
x95 = 12.0427718387609
x96 = 100.007366139275
x97 = 65.1007810993885
x98 = 56.025068989018
x99 = -57.7703982410123
x100 = 48.3456202802429
x100 = 48.3456202802429