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
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. 
.
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. 
.
9. 
.
10. 
.
11-12. Change from rectangular to spherical coordinates.
11. 
, 
so 
,
so 
(Note that 
because 
.)
Therefore, spherical coordinates of the given point are 
.
12. 
.
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. 
.
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
18. 
19. 
20. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
