# Homework Help: Parametric representation

1. Dec 6, 2005

### 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!

2. Dec 6, 2005

### hypermorphism

That should be y=4sin(phi)sin(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 ?

3. Dec 7, 2005

### 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 $\theta$?