Question 1182618
the angle is equal to 2pi/3.
convert to degrees and the angle is 2pi/3 * 180/pi = 2 * 180/3 = 2 * 60 = 120 degrees.


120 degrees is in the second quadrant.
the reference angle is 180 - 120 = 60 degrees.
that's the equivalent angle in the first quadrant.


the trig functions for a 60 degree angle are:


sin(60) = sqrt(3)/2
cos(60) = .5
tan(60) = sqrt(3)
cot(60) = sqrt(3)/3
sec(60) = 2
cosec(60) = 2 * sqrt(3)/3


the trig function for 120 degrees will be the same except for the sign.


in the second quadrant:
sin and cosec are positive
cos and sec are negative
tan and cot are negative.


therefore, you get:
sin(120) = sqrt(3)/2
cos(120) = -.5
tan(120) = -sqrt(3)
cot(120) = -sqrt(3)/3
sec(120) = -2
cosec(120) = 2 * sqrt(3)/3


translate back to radians and you get:


sin(2pi/3) = sqrt(3)/2
cos(2pi/3) = -.5
tan(2pi/3) = -sqrt(3)
cot(2pi/3) = -sqrt(3)/3
sec(2pi/3) = -2
cosec(2pi/3) = 2 * sqrt(3)/3