# For what values of x, if any, does f(x) = 1/((x-4)sinx)  have vertical asymptotes?

$x = 4 \mathmr{and} x = k \pi , k \in \mathbb{Z}$
This is hence when $\left(x - 4\right) = 0 \mathmr{and} \sin x = 0$
ie, when $x = 4 \mathmr{and} x = 0 + k \pi , k \in \mathbb{Z}$