Step 1
Remove full rotations of 360 degrees until the angle is between 0 and 360 degrees
[tex]480-360=120^o[/tex]Step 2
Hence, we find sin 120 using reference angles in the first quadrant
[tex]\begin{gathered} \sin \text{ 60=}\frac{\sqrt[]{3}}{2} \\ \text{Hence} \\ \sin 120=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sin 480=\sin 120=\sin 60=\frac{\sqrt[]{3}}{2} \\ \sin \text{ 480=}\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Answer sin 480 =(√3)/2
