Asosiy tarkibga o'tish

9.6-bo'lim : Qutb koordinatalari

15. Quyidagi qutb tenglamasining grafigini chizing.

\[r = 5 - 2\sin \theta \]
Yechim

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

\(\theta \) \(r\) \(\left( {r,\theta } \right)\)
0 5 \(\left( {5,0} \right)\)
\(\displaystyle \frac{\pi }{2}\) 3 \(\left( {3,\displaystyle \frac{\pi }{2}} \right)\)
\(\pi \) 5 \(\left( {5,\pi } \right)\)
\(\displaystyle \frac{{3\pi }}{2}\) 7 \(\left( {7,\displaystyle \frac{{3\pi }}{2}} \right)\)
\(2\pi \) 5 \(\left( {5,2\pi } \right)\)

Shunday qilib, bu funktsiyaning grafigi.

The graph of \(r = 5 - 2\sin \theta \). It is a rounded, almost circular curve rather than a strongly heart shaped one, sitting slightly above center, and the points \(\left( {5,0} \right)\), \(\left( {3,\frac{\pi }{2}} \right)\), \(\left( {5,\pi } \right)\) and \(\left( {7,\frac{{3\pi }}{2}} \right)\) 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.

Bundan tashqari, ushbu grafiklarning aksariyati noaniq yurak shaklida bo'lsa-da, bu eskiz ko'pchilik ko'rsatganidek va bu yurak shakliga qaraganda aylana shaklida.