12.12-bo'lim : Silindrsimon koordinatalar

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

1. \(\left( { - 3,5, - 8} \right)\)
2. \(\left( {4,1,7} \right)\)
3. Dekart koordinatalarida yozilgan quyidagi tenglamani Silindr koordinatalaridagi tenglamaga aylantiring. \(\displaystyle \frac{{x - y}}{{{x^2} + {y^2} + 1}} = xyz\)

4-6-masalalar uchun Silindr koordinatalarida yozilgan tenglamani Dekart koordinatalaridagi tenglamaga aylantiring.

1. \(z{r^3}\cos \left( \theta \right) = 4r + 8\)
2. \({r^2} - 3\sin \left( \theta \right) = {z^3} + \sqrt {{r^2} + 1} \)
3. \(\tan \left( \theta \right) + 2z = 1 - {r^2}\)

7-9-masalalar uchun berilgan tenglama bilan hosil qilingan sirtni aniqlang.

1. \(z = - 4r,\,\,\,z < 0\)
2. \(\displaystyle 2r + 6\cos \left( \theta \right) + 18\sin \left( \theta \right) = \frac{{51}}{r}\)
3. \(\theta = \frac{\pi }{3}\)