How do I find sin (-17pi/3) ?

Since it's negative you just go clockwise instead of counterclockwise around the circle. One full revolution is - 6pi/3, two revolutions are - 12pi/3, three would be - 18pi/3. This tells you it's pi/3 shy of being 3 full revolutions sin - 17pi/3 would be the same as pi/3.

Sin pi/3 = 1/2