Finding the Interval for Theta in Parametric Representation of a Sphere

[eunhye732]

Find the parametric representation for the surface:
The part of the sphere x^2 + y^2 + z^2 = 16 that lies between the planes z = -2 and z = 2.

okay, i know that i have to use spherical coordinates which is
x = 4sin(phi)cos(theta)
y = 4sin(phi)sin(phi)
z = 4cos(phi)

i know how to find the interval for phi, but how do you find the interval for theta? this is probably a stupid question, but i don't get it.
thanks!

 

[hypermorphism]

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y = 4sin(phi)sin(phi)
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That should be y=4sin(phi)sin(theta).

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i know how to find the interval for phi, but how do you find the interval for theta?
...

What is theta on the sphere ? If you set phi to some constant, what curve results on the sphere's surface ? What does this imply about the restriction on theta ?

 

[HallsofIvy]

Remember that $\theta$ measures the angle in a plane parallel to the xy plane. Imagine the sphere cut by such a plane for z between -2 and 2. What restrictions are there on $\theta$?