How to find cos(-19pi/6)

Use the unit circle.

-19pi/6 is the same as 3pi + pi/6
This means that it goes around the unit circle 3pi times and ends up at 7pi/6

So -19pi/6 is equivalent to 7pi/6.

Looking at the unit circle, cos(7pi/6) = -√3/2

Here for a good time of free question