Answer
$\frac{1}{2}$
Work Step by Step
To find exact value of $\sin 390^{\circ}$, let's find its co-terminal angle between $0^{\circ}$ and $360^{\circ}$ first-
Co-terminal angle of $390^{\circ}$ = $390^{\circ} - 360^{\circ}$ = $30^{\circ}$
Therefore
$\sin 390^{\circ}$ = $\sin 30^{\circ}$
($30^{\circ}$ and $390^{\circ}$ are co-terminal and trigonometric functions of co-terminal angles are same)
As $ 390^{\circ}$ terminates in quadrant I, its $\sin$ will be positive.
Therefore-
$\sin 390^{\circ}$ = $\sin 30^{\circ}$ = $\frac{1}{2}$
