Answer
$\cot$ 2280$^{\circ}$ = -$\frac{\sqrt3}{3}$
Work Step by Step
$\cot$ 2280$^{\circ}$
First, lets find the coterminal angle.
2280$^{\circ}$ - 6(360$^{\circ}$) = 120$^{\circ}$
Next, we find the reference angle.
$\theta$$^{1}$ = 180$^{\circ}$ - 120$^{\circ}$ = 60$^{\circ}$
Since the coterminal angle is in Quadrant II, $\cot$ is negative.
Therefore:
$\cot$ 60$^{\circ}$ = -$\frac{1}{\sqrt3}$ = -$\frac{\sqrt3}{3}$
