Asosiy tarkibga o'tish

9.6-bo'lim : Qutb koordinatalari

14. Quyidagi qutb tenglamasining grafigini chizing.

\[r = 8 + 8\cos \theta \]
Yechim

Biz ushbu bo'limdagi eslatmalardan bilamizki, bu kardioiddir va shuning uchun grafikni olish uchun bizga kerak bo'lgan narsa - nuqtalarning tezkor jadvali.

\(\theta \) \(r\) \(\left( {r,\theta } \right)\)
0 16 \(\left( {16,0} \right)\)
\(\displaystyle \frac{\pi }{2}\) 8 \(\left( {8,\displaystyle \frac{\pi }{2}} \right)\)
\(\pi \) 0 \(\left( {0,\pi } \right)\)
\(\displaystyle \frac{{3\pi }}{2}\) 8 \(\left( {8,\displaystyle \frac{{3\pi }}{2}} \right)\)
\(2\pi \) 16 \(\left( {16,2\pi } \right)\)

Shunday qilib, bu funktsiyaning grafigi.

The graph of \(r = 8 + 8\cos \theta \).  It is a cardioid that comes to a point at the origin on the left and bulges out to the right, reaching \(\left( {16,0} \right)\), and the points \(\left( {16,0} \right)\), \(\left( {8,\frac{\pi }{2}} \right)\), \(\left( {0,\pi } \right)\) and \(\left( {8,\frac{{3\pi }}{2}} \right)\) 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.