If $\tan \theta =-4/3$ then sin $\theta$ is 

Since $\tan \theta =-4/3$ which is negative. Hence $\theta$ either lies in the second quadrant or fourth quadrant. Hence $\sin \theta =4/5$ (when $\theta$ is in the second quadrant) or $\sin \theta =-4/5$ (when $\theta$ is in fourth quadrant).