3. 3
2 2
2 2
1, 3, 5
(1) 3 10
3.16
Given
x y z
x y
4. 4
1 1
1 0
0
1, 3, 5
3
tan tan
1
tan (3) 72
( , , ) (3.16,72 ,5)
Given
x y z
y
x
z
2 2 2
1, 3, 5
1 9 25 35
5.92
Given
x y z
r x y z
5. 5
2 2
1
1 1
0
0 0
1, 3, 5
tan
10
tan tan 0.6324
5
32.5
( , , ) (5.92,32.5 ,72 )
Given
x y z
x y
z
r
Convert point T(0, -4, 3) from
Cartesian to cylindrical and
spherical coordinates.
Solution
2 2
2 2
0, 4, 3
(0) ( 4) 16
4
Given
x y z
x y
6. 6
1 1
1 0
0
0, 4, 3
4
tan tan
0
tan ( ) 270
( , , ) (4,270 ,3)
Given
x y z
y
x
z
2 2 2
0, 4, 3
0 16 9 25
5
Given
x y z
r x y z
7. 7
2 2
1
1 1
1 0
0 0
0, 4, 3
tan
16 4
tan tan
3 3
tan 1.33 53.5
( , , ) (5,53.5 ,270 )
Given
x y z
x y
z
r
Convert point S(-3, -4, -10) from
Cartesian to cylindrical and
spherical coordinates.
Solution
8. 8
2 2
2 2
3, 4, 10
( 3) ( 4) 25
5
Given
x y z
x y
1 1
1 0
0
3, 4, 10
4
tan tan
3
tan (1.33) 233.5
( , , ) (5,233.5 , 10)
Given
x y z
y
x
z
9. 9
2 2 2
3, 4, 10
9 16 100 125
5 5 11.18
Given
x y z
r x y z
2 2
1
1 1
0
0 0
3, 4, 10
tan
25
tan tan ( 0.5)
10
153.5
( , , ) (11.18,153.5 ,233.5 )
Given
x y z
x y
z
r