El profesor se sorprenderá mucho al ver tu solución correcta😉
(cos(t) + 2)*3*k - 2*sin(t) = 0
suma
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\ | | / 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 //
=
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\ | | / 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 //
producto
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ | | | / 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 ///
=
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ | | | / 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*(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 //
/ / ___________\\ / / ___________\\ | | / 2 || | | / 2 || | |2 + \/ 4 - 27*k || | |2 + \/ 4 - 27*k || t2 = 2*re|atan|------------------|| + 2*I*im|atan|------------------|| \ \ 3*k // \ \ 3*k //
t2 = 2*re(atan((sqrt(4 - 27*k^2) + 2)/(3*k))) + 2*i*im(atan((sqrt(4 - 27*k^2) + 2)/(3*k)))