1. ## One Half-Angle Queston

Question...
For the Half-Angle Problems:

how do you know if the answer is positve or negative...
(i circled it in RED)

2. Originally Posted by CONFUSED_ONE
Question...
For the Half-Angle Problems:

how do you know if the answer is positve or negative...
(i circled it in RED)
It depends in which quadrant is $\displaystyle \frac{a}{2}$.
NOT $\displaystyle a$ but $\displaystyle \frac{a}{2}$.

If $\displaystyle \frac{a}{2}$ is in the first or second quadrant then you use positive, otherwise use the negative.
Your question, is a classic mistake which I seen many people make, hopefully you will not make it.

3. for example, what if a=4/5. so it'll be (4/5)/2 and that'll turn out to be 2/5. how do i know if 2/5 is in the first or second quadrant?

4. Originally Posted by CONFUSED_ONE
for example, what if a=4/5. so it'll be (4/5)/2 and that'll turn out to be 2/5. how do i know if 2/5 is in the first or second quadrant?
I presume that is in radians?
The first and second quadrant span $\displaystyle 0^o\leq x\leq 180^o$
Or in Radians, $\displaystyle 0\leq x\leq \pi$
Since,
$\displaystyle 0\leq .4\leq 3.14$ it is in the first and second quadrants.

In fact it is in first quadrant because it spans,
$\displaystyle 0\leq x\leq \frac{\pi}{2}\approx 1.57$