Question

how do i compute the exact value of sin(-10pi/3)

Answer 1

like I pointed out to earlier sin(x) = sin(x + 2pi)

So sin(-10pi/3) = sin(-10pi/3 + 4pi) = sin(2pi/3)

Now figure out that.

Answer 2

sin(-10pi/3)
=sin(-10pi/3+4pi) (periodic function)
=sin(2pi/3)
=sin(pi/3)
=sqrt(3)/2