Hi. I am having some trouble making sense out of something from my book..1

Question

Hi. I am having some trouble making sense out of something from my book..1<=2cosu<=2.
When they solve for theta they say the bounds are 0<=u<=pi/3 which seems wrong to me.

anonymous · Answer

Sorry that was suposed to be a 2

phi · Answer

are you sure it is 
$$ 1 \le 2 \cos u \le 2 $$
they start with ?

anonymous · Answer

Yeah I sure think so. I am parameterizing a sphere x^2 +y^2 +z^2=4 with the constraint 1<=z<=2. When I paramaterize sphere I get r(u,v)=<2sinucosu,2sinusinv,2cosu>. Since 1<=z<=2 and Z=2cosu.
1<=2cosu<=2

phi · Answer

if so, divide by 2 to get
$$ \frac{1}{2} \le \cos u \le 1 $$
take the inverse cos of both limits
to get
pi/3 and 0
which means u >=0  and u<= pi/3

anonymous · Answer

So isn't that pi/3<=u<=2pi?

anonymous · Answer

just don't understand how it seems the direction changes?

anonymous · Answer

Do the < change direction when taking inverse cos?

phi · Answer

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