(cos(t)+2)*3*k-2*sin(t)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Suma y producto de raíces
[src]
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||
- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| + 2*re|atan|------------------|| + 2*I*im|atan|------------------||
\ \ 3*k // \ \ 3*k // \ \ 3*k // \ \ 3*k //
(−2re(atan(3k4−27k2−2))−2iim(atan(3k4−27k2−2)))+(2re(atan(3k4−27k2+2))+2iim(atan(3k4−27k2+2)))
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| |-2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||
- 2*re|atan|-------------------|| + 2*re|atan|------------------|| - 2*I*im|atan|-------------------|| + 2*I*im|atan|------------------||
\ \ 3*k // \ \ 3*k // \ \ 3*k // \ \ 3*k //
−2re(atan(3k4−27k2−2))+2re(atan(3k4−27k2+2))−2iim(atan(3k4−27k2−2))+2iim(atan(3k4−27k2+2))
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\
| | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 |||
| | |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k ||| | | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k |||
|- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|||*|2*re|atan|------------------|| + 2*I*im|atan|------------------|||
\ \ \ 3*k // \ \ 3*k /// \ \ \ 3*k // \ \ 3*k ///
(−2re(atan(3k4−27k2−2))−2iim(atan(3k4−27k2−2)))(2re(atan(3k4−27k2+2))+2iim(atan(3k4−27k2+2)))
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\
| | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 |||
| | |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k ||| | | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k |||
-4*|I*im|atan|-------------------|| + re|atan|-------------------|||*|I*im|atan|------------------|| + re|atan|------------------|||
\ \ \ 3*k // \ \ 3*k /// \ \ \ 3*k // \ \ 3*k ///
−4(re(atan(3k4−27k2−2))+iim(atan(3k4−27k2−2)))(re(atan(3k4−27k2+2))+iim(atan(3k4−27k2+2)))
-4*(i*im(atan((-2 + sqrt(4 - 27*k^2))/(3*k))) + re(atan((-2 + sqrt(4 - 27*k^2))/(3*k))))*(i*im(atan((2 + sqrt(4 - 27*k^2))/(3*k))) + re(atan((2 + sqrt(4 - 27*k^2))/(3*k))))
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |-2 + \/ 4 - 27*k || | |-2 + \/ 4 - 27*k ||
t1 = - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------||
\ \ 3*k // \ \ 3*k //
t1=−2re(atan(3k4−27k2−2))−2iim(atan(3k4−27k2−2))
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k ||
t2 = 2*re|atan|------------------|| + 2*I*im|atan|------------------||
\ \ 3*k // \ \ 3*k //
t2=2re(atan(3k4−27k2+2))+2iim(atan(3k4−27k2+2))
t2 = 2*re(atan((sqrt(4 - 27*k^2) + 2)/(3*k))) + 2*i*im(atan((sqrt(4 - 27*k^2) + 2)/(3*k)))