12.12-bo'lim: Silindrsimon koordinatalar

1 va 2-masalalar uchun nuqta uchun Dekart koordinatalarini silindrsimon koordinatalarga aylantiring.

1. \(\left( {4, - 5,2} \right)\) Yechim
2. \(\left( { - 4, - 1,8} \right)\) Yechim
3. Dekart koordinatalarida yozilgan quyidagi tenglamani Silindr koordinatalaridagi tenglamaga aylantiring. \[{x^3} + 2{x^2} - 6z = 4 - 2{y^2}\] Yechim

4 va 5-masalalar uchun Silindr koordinatalarida yozilgan tenglamani Dekart koordinatalaridagi tenglamaga aylantiring.

1. \(z\,r = 2 - {r^2}\) Yechim
2. \(\displaystyle 4\sin \left( \theta \right) - 2\cos \left( \theta \right) = \frac{r}{z}\) Yechim

6 va 7-masalalar uchun berilgan tenglama tomonidan hosil qilingan sirtni aniqlang.

1. \({r^2} - 4r\cos \left( \theta \right) = 14\) Yechim
2. \(z = 7 - 4{r^2}\) Yechim