TRIGONOMENTRY HELP

[Guest]

give the eact value of
sin 4pie / 3

the answer is -root 3 / 2

and i have no idea how to get to the answer

 

[tkhunny]

Think "Reference Angle"

sin(-4*pi/3) = -sin(2pi/3) = -sin(pi/3) = -sqrt(3)/2

 

[Gene]

2*pi/3 = 120°
(I think better in degrees)
So you have a line at 2*120 = 240° (third quadrant) or 60° down from the x axis. An old friend. A 30-60-90 triangle.
x=-1,y=-sqrt(3),hypot=2
sin = opposite/hypot =
-sqrt(3)/2