Question 1182618: Evaluate the six trigonometric function of: s=2π/3. Show your solution.
1. sin s =
cos s =
tan s =
cot s =
csc s =
sec s =
Found 2 solutions by Theo, Edwin McCravy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website! Evaluate the six trigonometric function of: s=2π/3. Show your solution.
 is 120o, has a referent angle of 60o and is in the second quadrant,
so we draw a 30-60-90 triangle with hypotenuse=r=2, adjacent=x=1, and
opposite=y=√3
However, x goes left in QII, so we must make x negative, so we have x=-1
instead of 1 in the graph below. y is positive because it goes upward.
r, the hypotenuse or radius vector is always taken positive in all quadrants.
adjacent = x = -1, opposite = y = √3, hypotenuse = r = 2
Edwin
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