Asosan, bu erda qilishimiz kerak bo'lgan narsa barcha \(x\) va \(y\) ni quyidagi formulalar yordamida \(r\) va \(\theta \) ga aylantirishdir.

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

Oxirgi haqida unutmang! Agar ushbu formuladan foydalanish mumkin bo'lsa (va siz buni qaerda ishlatishimizni ko'rishingiz mumkin, shunday emasmi?) bu juda ko'p ishni tejaydi!

Birinchidan, kerak bo'lganda tenglamalarni almashtiramiz.

\[\frac{{4\left( {r\cos \theta } \right)}}{{3{r^2}}} = 6 - \left( {r\cos \theta } \right)\left( {r\sin \theta } \right)\]

Nihoyat, biz qilishimiz kerak bo'lgan narsaga erishish uchun ozgina soddalashtirishga e'tibor berishimiz kerak,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{4\cos \theta }}{{3r}} = 6 - {r^2}\cos \theta \sin \theta }}\]