Answer
$sin \space t \gt 0$
$sec \space t = -5/3$
$csc \space t \gt 0$
$cot \space t \lt 0$
Work Step by Step
$$tan \space t = \frac{sin \space t}{cos \space t} \longrightarrow sin \space t = tan \space t \space cos \space t$$
Since $cos \space t$ is negative (-3/5), and $tan \space t$ is negative, the result of the multiplication will be positive: $sin \space t \gt 0$
$$sec \space t = \frac{1}{cos \space t} = \frac{1}{-3/5} = -5/3$$ $$csc \space t = \frac{1}{sin \space t} $$
Since sin t is positive ($> 0$) and 1 is positive, the result of this division will also be positive. $csc \space t \gt 0$ $$cot \space t = \frac{1}{tan\space t}$$
Since 1 is positive and tan t is negative ($\lt 0$), the result of this division will be negative. $cot \space t \lt 0$
