12.13-bo'lim: Sferik koordinatalar

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

1. \(\left( {3, - 4,1} \right)\) Yechim
2. \(\left( { - 2, - 1, - 7} \right)\) Yechim
3. \(\left( {2,0.345, - 3} \right)\) nuqtasi uchun silindrsimon koordinatalarni sferik koordinatalarga aylantiring. Yechim
4. Dekart koordinatalarida yozilgan quyidagi tenglamani Sferik koordinatadagi tenglamaga aylantiring. \[{x^2} + {y^2} = 4x + z - 2\] Yechim

5 va 6-masalalar uchun Sferik koordinatalarda yozilgan tenglamani Dekart koordinatalaridagi tenglamaga aylantiring.

1. \({\rho ^2} = 3 - \cos \varphi \) Yechim
2. \(\csc \varphi = 2\cos \theta + 4\sin \theta \) Yechim

7 va 8-masalalar uchun berilgan tenglama bilan hosil qilingan sirtni aniqlang.

1. \(\displaystyle \varphi = \frac{{4\pi }}{5}\) Yechim
2. \(\rho = - 2\sin \varphi \cos \theta \) Yechim