Given:
[tex]\sin 285^{\circ}[/tex]To express it as a function of reference angle:
Since the angle lies in the fourth quadrant.
So, the reference angle will be,
[tex]\begin{gathered} \theta_{ref}=360-\theta_4 \\ \theta_{ref}=360^{\circ}-285 \\ \theta_{ref}=75^{\circ} \end{gathered}[/tex]Therefore, the function of the reference angle is,
[tex]\sin 75^{\circ}[/tex]