Answer
$tan \space t \lt 0$
$csc \space t = -2$
$sec \space t \gt 0$
$cot \space t \lt 0$
Work Step by Step
$$tan \space t = \frac{sin \space t}{cos \space t} $$
Since $sin \space t$ is negative (-1/2), and $cos \space t$ is positive, the result of the division will be negative: $tan \space t \lt 0$
$$csc \space t = \frac{1}{sin\space t} = \frac{1}{-1/2} = -2$$ $$sec \space t = \frac{1}{cos \space t} $$
Since cos t is positive ($> 0$) and 1 is positive, the result of this division will also be positive. $sec \space t \gt 0$ $$cot \space t = \frac{1}{tan\space t}$$
Since 1 is positive and tan t is negative ($\lt 0$), the result of this division will be negative. $cot \space t \lt 0$
