Question

How do I get the exact value of sin 480?

Answer 1

Step 1

Remove full rotations of 360 degrees until the angle is between 0 and 360 degrees

`480-360=120^o`

Step 2

Hence, we find sin 120 using reference angles in the first quadrant

`\begin{gathered} \sin \text{ 60=}\frac{\sqrt[]{3}}{2} \\ \text{Hence} \\ \sin 120=\frac{\sqrt[]{3}}{2} \end{gathered}`

Therefore,

`\begin{gathered} \sin 480=\sin 120=\sin 60=\frac{\sqrt[]{3}}{2} \\ \sin \text{ 480=}\frac{\sqrt[]{3}}{2} \end{gathered}`

Answer sin 480 =(√3)/2