12.13-bo'lim : Sferik koordinatalar
3. \(\left( {2,0.345, - 3} \right)\) uchun silindrsimon koordinatalarni sferik koordinatalarga aylantiring.
Yechim
Bizga berilgan nuqtadan boshlab,
\[r = 2\hspace{0.5in}\theta = 0.345\hspace{0.5in}z = - 3\]Shunday qilib, biz allaqachon Sferik koordinatalar uchun \(\theta \) qiymatiga egamiz.
2-qadam
Keyinchalik, biz \(\rho \) ni aniqlashimiz mumkin.
\[\rho = \sqrt {{{\left( 2 \right)}^2} + {{\left( { - 3} \right)}^2}} = \sqrt {13} \]3-qadam
Nihoyat, biz \(\varphi \) ni aniqlashimiz mumkin.
\[\cos \varphi = \frac{z}{\rho } = \frac{{ - 3}}{{\sqrt {13} }}\hspace{0.5in}\varphi = {\cos ^{ - 1}}\left( {\frac{{ - 3}}{{\sqrt {13} }}} \right) = 2.5536\]Sferik koordinatalar u holda,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{\left( {\sqrt {13} ,0.345,2.5536} \right)}}\]