Calculus-Sec-14-4-Solution
14.4 Cylindrical Coordinates and Spherical Coordinates
by SGLee - HSKim -SWSun
1-4. Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point.
1.
http://matrix.skku.ac.kr/cal-lab/cal-14-2-1.html
2.
3.
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4.
Answer: .
5-6.Change from rectangular to cylindrical coordinates.
5.
, so , .
Therefore one set of cylindrical coordinates is . Another is .
As with polar coordinates, there are infinitely many choices.
6.
7-10. Plot the point whose spherical coordinates are given. Then, find the rectangular coordinates of the point.
7.
http://matrix.skku.ac.kr/cal-lab/cal-14-2-7.html
8.
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9.
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10.
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11-12. Change from rectangular to spherical coordinates.
11.
, so ,
so (Note that because .)
Therefore, spherical coordinates of the given point are .
12.
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13-14. Change from cylindrical to spherical coordinates.
13.
, , , . So, , and .
Therefore, rectangular coordinates are and .
, so .
, so ( because ).
Therefore, spherical coordinates of the given point are and .
14.
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15-16. Change from spherical to cylindrical coordinates.
15.
, , , .
So, , since , .
Therefore, rectangular coordinates are
, , so .
Therefore cylindrical coordinates of the given point are .
16.
, ,
Therefore rectangular coordinates of the given point are .
, , so .
Therefore cylindrical coordinates of the given point are .
17-20. Describe in words the surface whose equation is given.
17.
http://matrix.skku.ac.kr/cal-lab/cal-14-2-17.html
21-28. Identify the surface whose equation is given.
21.
http://matrix.skku.ac.kr/cal-lab/cal-14-2-21.html