Answer
$\sin$ 1305$^{\circ}$ = $\frac{-\sqrt2}{2}$
Work Step by Step
$\sin$ 1305$^{\circ}$
First, lets find the coterminal angle.
1305$^{\circ}$ - 3(360$^{\circ}$) = 225$^{\circ}$
Next, we find the reference angle.
$\theta$$^{1}$ = 225$^{\circ}$ - 180$^{\circ}$
$\theta$$^{1}$ = 45$^{\circ}$
Since the coterminal angle is in Quadrant III, $\sin$ is negative.
Therefore:
$\sin$ 45$^{\circ}$ = $\frac{-1}{\sqrt2}$ = $\frac{-\sqrt2}{2}$
