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## Homework Statement

I am confused about spherical coordinates stuff. For example, we can parametrize a sphere of radius 3 by

[itex] x = 3 sin \phi cos \theta [/itex]

[itex] y = 3 sin \phi sin \theta [/itex]

[itex] z = 3cos\phi [/itex]

where [itex] 0 \le \theta \le 2 \pi [/itex] and [itex] 0 \le \phi \le \pi [/itex] .

I don't understand about the range of [itex] \phi [/itex].

1) Why is [itex] 0 \le \phi \le \pi [/itex] ?

2) If we only want the lower hemisphere, why is the range now [itex] \frac{\pi}{2} \le \phi \le \pi [/itex] ?

3) What about the range of [itex] \phi [/itex] if we want the upper hemisphere?

Is there any place where I get to see the diagram so I can get the picture better?

Thanks!