Need help with a trig problem, will FAN and MEDAL. Problem will be in comments

Question

anonymous · Answer

$$\sin \theta=\frac{ -4 }{ 5 } \  ,  \frac{ -\pi }{ 2 }<\theta<0$$

$$\cos \beta=\frac{ -5 }{ 13 }  ,  \frac{ \pi }{ 2 }<\beta<\pi$$

What is cos theta/2? I tried it and I need to check my answer

anonymous · Answer

$$\huge \sqrt{\frac{1+\frac{3}{5}}{2}}$$ i thinkor maybe it is negative

anonymous · Answer

$\theta$ is in quadrant 4, making $\cos(\theta)$ positive 
$$\sin(\theta)=-\frac{4}{5}\implies \cos(\theta)=\frac{3}{5}$$

anonymous · Answer

plug in the the half angle formula and you get what i wrote above, except it is $\pm$ and we have to figure out whether it is positive or negative

anonymous · Answer

i guess positive, because if $$-\frac{\pi}{2}<\theta<0$$ then also 
$$-\frac{\pi}{2}<\frac{\theta}{2}<0$$

anonymous · Answer

also you have some arithmetic to do,  i will leave that up to you

anonymous · Answer

In the end I came up with 
$$2\sqrt{5} / 5$$