12.13-bo'lim : Sferik koordinatalar

1-3-masalalar uchun nuqta uchun Dekart koordinatalarini Sferik koordinatalarga aylantiring.

1. \(\left( {6,2, - 8} \right)\)
2. \(\left( { - 1,5,2} \right)\)
3. \(\left( { - 3, - 2,1} \right)\)
4. \(\left( {5,1.294,6} \right)\) nuqtasi uchun silindrsimon koordinatalarni sferik koordinatalarga aylantiring.
5. Dekart koordinatalarida yozilgan quyidagi tenglamani Sferik koordinatadagi tenglamaga aylantiring. \[\frac{{xz}}{y} = 2 - x\]

6 – 8 masalalar uchun Sferik koordinatalarda yozilgan tenglamani Dekart koordinatalaridagi tenglamaga aylantiring.

1. \(\rho \cos \varphi \sin \varphi \sin \theta = 3\)
2. \(\rho - \cos \varphi = 2 + {\cos ^2}\varphi \)
3. \(\tan \varphi \left( {\cos \theta - \sin \theta } \right) = 4\)

9 va 10-masalalar uchun berilgan tenglama bilan hosil qilingan sirtni aniqlang.

1. \({\cos ^2}\varphi - {\sin ^2}\varphi = 0\)
2. \(\displaystyle \sin \varphi cos\theta + sin\varphi sin\theta + \cos \varphi = \frac{1}{\rho }\)