No it wouldn't...
cos theta = adj / hyp = ( -1/9)/2 [which would simplify to -1/18]
If \(cos\theta = (-1/9)/2\)
then what is
\(acos ((-1/9)/2)\) ?
Maybe it might help to think of it as an equation
\(\qquad cos \theta = ((-1/9)/2)\\ so\\ acos[cos \theta] = acos ((-1/9)/2)\\ \qquad \qquad\theta= acos ((-1/9)/2)\\ \qquad \text{[since acos and cos cancel each other out.]}\)
You have my right angle triangle diagram with theta on it.
Work out the third side using pythagoras.
Then read sin(theta) off it.