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9.6-bo'lim : Qutb koordinatalari

16. Quyidagi qutb tenglamasining grafigini chizing.

\[r = 4 - 9\sin \theta \]
Yechim

Biz ushbu bo'limdagi eslatmalardan bilamizki, bu ichki halqaga ega limacon va shuning uchun grafikni olish uchun bizga kerak bo'lgan narsa nuqtalarning tezkor jadvalidir.

\(\theta \) \(r\) \(\left( {r,\theta } \right)\)
0 4 \(\left( {4,0} \right)\)
\(\displaystyle \frac{\pi }{2}\) -5 \(\left( { - 5,\displaystyle \frac{\pi }{2}} \right)\)
\(\pi \) 4 \(\left( {4,\pi } \right)\)
\(\displaystyle \frac{{3\pi }}{2}\) 13 \(\left( {13,\displaystyle \frac{{3\pi }}{2}} \right)\)
\(2\pi \) 4 \(\left( {4,2\pi } \right)\)

Shunday qilib, bu funktsiyaning grafigi.

The graph of \(r = 4 - 9\sin \theta \). It is a limaçon with a large outer loop that hangs down below the origin, reaching \(\left( {13,\frac{{3\pi }}{2}} \right)\) at the bottom, and a small inner loop above the origin. The points \(\left( {4,0} \right)\), \(\left( { - 5,\frac{\pi }{2}} \right)\), \(\left( {4,\pi } \right)\) and \(\left( {13,\frac{{3\pi }}{2}} \right)\) are marked and labeled on it.

Ushbu nuqtalarni chizishda ehtiyot bo'ling va qutb koordinatalarini chizish qoidalarini eslang. Grafikdagi "belgilar" haqiqatan ham Kartezian koordinata belgilaridir, chunki ular bizga tanish. Bizning eskizimiz uchun qutb nuqtalarini chizishga borganingizda, ular sizni chalkashtirib yuborishlariga yo'l qo'ymang.