Answer
$\tan(-6.29)$ is negative
Work Step by Step
The angles (in radians) representing borders between quadrants are
1. for positive angles, that is, radian measures
counted counterclockwise from the point (1,0) :
$[0]$ ... I ... $[\displaystyle \frac{\pi}{2}\approx 1.57]$
$[\displaystyle \frac{\pi}{2}\approx 1.57]$ ... II ... $[\pi\approx 3.14]$
$[\pi\approx 3.14]$ ... III ...$[\displaystyle \frac{3\pi}{2}\approx 4.71]$
$[\displaystyle \frac{3\pi}{2}\approx 4.71]$... IV... $2\pi\approx 6.28$
2. for negative (clockwise from the point (1,0)):
$[0]$ ... IV ... $[-\displaystyle \frac{\pi}{2}\approx-1.57]$
$[-\displaystyle \frac{\pi}{2}\approx-1.57]$ ... III ... $[-\pi\approx-3.14]$
$[-\pi\approx-3.14]$ ... II ...$[-\displaystyle \frac{3\pi}{2}\approx-4.71]$
$[-\displaystyle \frac{3\pi}{2}\approx-4.71]$... I... $[-2\pi\approx-6.28]$
------------
For any real number $s$ represented by a directed arc on the unit circle,
$\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$
=================
A radian measure of $-6.29 $ (clockwise)
is coterminal with an angle with radian measure $-6.29-6.28=-0.1$
which represents an angle in quadrant $IV$,
( radian measure of $-6.28$ means one whole revolution has been completed)
$-1.57 < -0.1 < 0$
in quadrant IV, x is positive, y is negative
which means that $ \displaystyle \frac{y}{x}$ is negative,
so
$\tan(-6.29)=\tan(-0.1)$ is negative