We know that the number pi=3.14 (approx.), so, if we'll calculate:
2pi=6.28 and 2*pi-pi/2=(3*pi)/2=1.5*pi=4.71
From the results above, 6 belongs to the interval (3pi/2,2pi), meaning 6 is in the IV-th quadrant.
In the IV-th quadrant, sine function is negative, so sin 6<0.
sin 6 = sin(6radian)
= sin (6*180/pi) = sin (sin 343.77...) = sin (-16.225..)
= -sin (16.225..). But sin16.225 nbeing in first quadrant is positive. Therefore, sin (6radians) is negative.