Step 1

Use \(\displaystyle{\sin{{\left({360}+\alpha\right)}}}={\sin{\alpha}}\)

Step 2

\(\displaystyle{\sin{{390}}}\)

\(\displaystyle={\sin{{\left({360}+{30}\right)}}}\)

\(\displaystyle={\sin{{30}}}\)

\(\displaystyle={\frac{{{1}}}{{{2}}}}={0.5}\)

Use \(\displaystyle{\sin{{\left({360}+\alpha\right)}}}={\sin{\alpha}}\)

Step 2

\(\displaystyle{\sin{{390}}}\)

\(\displaystyle={\sin{{\left({360}+{30}\right)}}}\)

\(\displaystyle={\sin{{30}}}\)

\(\displaystyle={\frac{{{1}}}{{{2}}}}={0.5}\)