I don't understand this statement on this website . Please help, this is about half-angle identities and +/-.

Question

anonymous · Answer

The statement in question is this: http://bit.ly/AuIXO0

nottim · Answer

Try Khan's Academy?

anonymous · Answer

I tried that, but there was nothing

nottim · Answer

no txtbook?

anonymous · Answer

No
Txtbook doesn't explain. Im confused about the +/- sign for the final answer. I do everything right except that.

phi · Answer

They ask about
Find the possible values of tan(1/2)theta when tantheta = 7/24

This means 
$$ tan(\theta) = \frac{7}{24} $$ 
or 
$$ tan(\theta) = \frac{-7}{-24} $$ 

The first angle is in the 1st quadrant and the half angle will be in the first quadrant

the second angle is in the third quadrant, and half of it is in the 2nd quadrant.  (So its tan will be negative)
|dw:1332113662460:dw|