Answer
$tan(-900^{\circ}) = 0$
Work Step by Step
Since each full rotation is $360^{\circ}$, the angle $-900^{\circ}$ is in the same position as $-900^{\circ}+n\times 360^{\circ}$ for any integer $n$.
When $n = 3$:
$\theta = -900^{\circ}+n\times 360^{\circ}$
$\theta = -900^{\circ}+(3)(360^{\circ})$
$\theta = 180^{\circ}$
For this angle, we can use the point (-1, 0).
x = -1
y = 0
r = 1
We can find the value of $tan(-900^{\circ})$:
$tan(-900^{\circ}) = \frac{y}{x}$
$tan(-900^{\circ}) = \frac{0}{-1} = 0$
