Answer
$\cos(6)$ is positive
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... $[-2\pi\approx-6.28]$
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For any real number $s$ represented by a directed arc on the unit circle,
$\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$
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A radian measure of $6 $ (counterclockwise)
represents an angle in quadrant IV,
$4.71 < 6 < 6.28$
where the x coordinate (the cosine) is positive,
so
$\cos(6)$ is positive
