Question

Given sin(alpha) = -4/5 and alpha is in qudrant 4, find the exact value of sin(alpha/2).

Answer 1

Alright, this has a few steps.

We'll use two equations:

\[\sin^2(\alpha) + \cos^2(\alpha) = 1\]
and
\[\sin(\frac{\alpha}{2}) = \pm \sqrt{\frac{1-\cos(\alpha)}{2}}\]

After finding the value for cosine, you can use the second equation to find the value you are looking for. Just be careful of which value to use (the plus/minus in front of the square root)! The quadrant you are in will tell you which one to use!