# Question #872b5

Oct 1, 2017

If $\cos a = - \frac{1}{3}$, $a$ must be between $90$ and $180$ degrees. In other words, a in $2$nd quadrant in unit circle. In this quadrant $\sin a > 0$. So, if $\cos a = - \frac{1}{3}$, $\sin a = \frac{2 \sqrt{2}}{3}$
After using $\sin 2 a = 2 \sin a \cdot \cos a$ identity, I found $\sin 2 a = - \frac{4 \sqrt{2}}{9}$
1) I found $\sin a$ after being given $\cos u = - \frac{1}{3}$ and $90 < a < 180$ conditions.
2) I used $\sin 2 a = 2 \sin a \cdot \cos a$ identity.