9.6-bo'lim: Qutb koordinatalari

1. \(\displaystyle \left( {2,\frac{\pi }{7}} \right)\) qutbli koordinatali nuqta uchun bir xil nuqta uchun uch xil koordinatalar to'plamini aniqlang, ularning barchasi burchaklari \(\displaystyle \frac{\pi }{7}\) dan farq qiladi va \( - 2\pi \le \theta \le 2\pi \) oralig'ida. Yechim
2. Nuqtaning qutb koordinatalari \(\left( { - 5,0.23} \right)\). Nuqta uchun dekart koordinatalarini aniqlang. Yechim
3. Nuqtaning kartezian koordinatasi \(\left( {2, - 6} \right)\). Nuqta uchun qutb koordinatalari to'plamini aniqlang. Yechim
4. Nuqtaning kartezian koordinatasi \(\left( { - 8,1} \right)\). Nuqta uchun qutb koordinatalari to'plamini aniqlang. Yechim

5 va 6-masalalar uchun berilgan tenglamani qutb koordinatalari bo'yicha tenglamaga aylantiring.

1. \(\displaystyle \frac{{4x}}{{3{x^2} + 3{y^2}}} = 6 - xy\) Yechim
2. \(\displaystyle {x^2} = \frac{{4x}}{y} - 3{y^2} + 2\) Yechim

7 va 8-masalalar uchun berilgan tenglamani dekart koordinatalari bo‘yicha tenglamaga aylantiring.

1. \(6{r^3}\sin \theta = 4 - cos\theta \) Yechim
2. \(\displaystyle \frac{2}{r} = \sin \theta - \sec \theta \) Yechim

9 – 16 masalalar uchun berilgan qutb tenglamasining grafigini chizing.

1. \(\displaystyle \cos \theta = \frac{6}{r}\) Yechim
2. \(\displaystyle \theta = - \frac{\pi }{3}\) Yechim
3. \(r = - 14\cos \theta \) Yechim
4. \(r = 7\) Yechim
5. \(r = 9\sin \theta \) Yechim
6. \(r = 8 + 8\cos \theta \) Yechim
7. \(r = 5 - 2\sin \theta \) Yechim
8. \(r = 4 - 9\sin \theta \) Yechim