Answer
$tan (-900^{\circ}) = \frac{sin (-900^{\circ})}{cos (-900^{\circ})} = \frac{0}{-1} = 0$
Work Step by Step
$sin (\theta) = \frac{y}{r}$
$cos (\theta) = \frac{x}{r}$
We can express $tan(\theta)$ using $sin(\theta)$ and $cos(\theta)$:
$tan (\theta) = \frac{y}{x}$
$tan (\theta) = \frac{y/r}{x/r}$
$tan (\theta) = \frac{sin (\theta)}{cos (\theta)}$
Therefore, if we know $sin (\theta)$ and $cos (\theta)$, then we can find $tan(\theta)$.
$tan (-900^{\circ}) = \frac{sin (-900^{\circ})}{cos (-900^{\circ})} = \frac{0}{-1} = 0$
