Ushbu muammoni hal qilishning turli usullari mavjud. Buning bir usuli - avval hamma narsani \(r\) ga ko'paytirish va keyin quyidagi tarzda biroz o'zgartirishni amalga oshirish:

\[6{r^4}\sin \theta = 4r - rcos\theta \hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}6{r^3}\left( {r\sin \theta } \right) = 4r - rcos\theta \hspace{0.25in}\]

Endi biz ushbu muammoni hal qilish uchun quyidagi formulalardan foydalanishimiz mumkin.

\[x = r\cos \theta \hspace{0.25in}\hspace{0.25in}y = r\sin \theta \hspace{0.25in}\hspace{0.25in}r = \sqrt {{x^2} + {y^2}} \]

Mana bu muammoning javobi,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{6y{{\left[ {\sqrt {{x^2} + {y^2}} \,} \right]}^3} = 4\sqrt {{x^2} + {y^2}} - x}}\]