Okay, here are the steps to solve this:
1) cos a = -5/9. This means cos a is negative, so the angle a lies in the 2nd or 3rd quadrant. Since the question specifies that a is in quadrant 3, we can take a as lying in the 3rd quadrant.
2) In the 3rd quadrant, cos a is negative and sin a is positive.
3) We know: cos a = adj/hyp. Here, adj = -5 and hyp = 9. So in a right-angled triangle with hypotenuse 9, the adjacent side is 5.
4) Use the Pythagorean theorem: a^2 + b^2 = c^2. Here, 5^2 + b^2 = 9^2.
So b^2 = 64 and b = 8.
5) Now sin a = opp/adj = b/hyp = 8/9.
6) Therefore, the exact value of sin a is 8/9.
Does this make sense? Let me know if you have any other questions!