Answer
$-\frac{3}{5}$
Work Step by Step
Recall the identity $\sin^{2}\theta+\cos^{2}\theta=1$
$\implies (\frac{4}{5})^{2}+\sin^{2}\theta=1$
$\implies \sin^{2}\theta=1-\frac{16}{25}=\frac{9}{25}$
$\implies \sin\theta=\pm\frac{3}{5}$
$\sin\theta$ is negative in the fourth quadrant.
$\implies\sin\theta=-\frac{3}{5}$
