Use spherical coordinates to describe the region above xy-plane

[whig4life]

Question: "Use spherical coordinates to describe the region above the xy plane between the spheres of radius 1 and 3 centered at the origin,"

My attempt: I know this means that 1 ≤ ρ ≤ 3, aside from that I do not know what else to describe? Does anyone have some insight?

 

[Deleted member 4993]

Question: "Use spherical coordinates to describe the region above the xy plane between the spheres of radius 1 and 3 centered at the origin,"

My attempt: I know this means that 1 ≤ ρ ≤ 3, aside from that I do not know what else to describe? Does anyone have some insight?

What about the angles - Θ and Φ?

If Φ is the angle from z-axis (azimuthal) - then you have 0 ≤ Φ ≤ π/2

You think about Θ (the angle in x-y plane).......

 

[whig4life]

What about the angles - Θ and Φ?

If Φ is the angle from z-axis (azimuthal) - then you have 0 ≤ Φ ≤ π/2

You think about Θ (the angle in x-y plane).......

Is "0 ≤ Θ ≤ π/2" as well?

 

[whig4life]

^I say that because π/2 is 90°

 

[HallsofIvy]

No, that is incorrect. \(\displaystyle \phi\) goes from 0 to \(\displaystyle \frac{\pi}{2}\) because it normally goes from 0 to \(\displaystyle \pi\) but here you have only \(\displaystyle z\ge 0\).

Now, what is the normal range for \(\displaystyle \theta\) in spherical coordinates? Is there any geometric reason to restrict it?