Answer
negatve
Work Step by Step
see: Signs of the Trigonometric Functions (p.412)
$\left[\begin{array}{lll}
Quadrant & Positive & Negative\\
I & all & none\\
II & sin, csc & cos, sec, tan, cot\\
III & tan, cot & sin, csc, cos, sec\\
IV & cos, sec & sin, csc, tan, cot
\end{array}\right]$
In quadrant $III$,
$\tan t$ is positive,
$\sin t$ is negative
$\cot t $is positive
The expression $\displaystyle \frac{\tan t\sin t}{\cot t}$
has an odd number (1) of negative factors,
Its sign is negative
