change from rectangular to spherical coordinates (xy\' z) = (1-4 (b) (2, 7x/4, R

Question

change from rectangular to spherical coordinates (xy' z) = (1-4 (b) (2, 7x/4, R/3) (x, y, z) " (1 Change from rectangular to spherical coordinates. (a) (. v3. 2v3) (a, , ) = (14 Submit Answer Save ProgressPractioe Another Version , 10110 points t Previous Answers scaleccs 7AE 02 . EXAMPLE 2 Describe the surface whose equation in cylind SOLUTION The equation says that the z-value of each point Because doesn't appear, it can vary. So any horizontal trac These traces suggest that the surface is Online Textbook coordinates. Thus vie have Type here to search

Explanation / Answer

in spherical coordinates :=(x2+y2+z2),=tan-1(y/x),= cos-1(z/)

(a)

(x,y,z)=(1,3 ,23)

=(12+(3)2+(23)2)

=(1+3+12)

=4

=tan-1(3/1)

=(/3)

= cos-1(23/4)

= cos-1(3/2)

= (/6)

(,,)=(4,/3,/6)

----------------------------------------------

(b)

(x,y,z)=(0,3 ,3)

=(02+(3)2+(3)2)

=32

=tan-1(3/0)

=(/2)

= cos-1(3/32)

= cos-1(1/2)

= (/4)

(,,)=(32,/2,/4)

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