SOLUTION: How do I get the correct answer to these types of problems? It says to evaluate by use of the reference angle (arc), if applicable. cos(8pi/3) another is sin (5pi/3). How

Question 428535: How do I get the correct answer to these types of problems?
It says to evaluate by use of the reference angle (arc), if applicable.
cos(8pi/3)
another is sin (5pi/3).
How do I find these using the ref angle? thanks!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How do I get the correct answer to these types of problems?
It says to evaluate by use of the reference angle (arc), if applicable.
cos(8pi/3)
another is sin (5pi/3).
How do I find these using the ref angle?
..
cos(8pi/3)
Think (8pi/3) as 3+2/3 pi
For each pi,you rotate the the terminating side 180 deg cc starting from the initial side at zero deg.
So, for 3 pi, you complete one rotation plus 180 deg which puts the terminating side at 180 deg, but you still have 2/3 pi to go which is two pi/3 (60 deg) or 120 deg. The terminating side is now at 300 (180+120) deg which makes a reference angle of 60 deg with the x-axis in the 4th quadrant. Hence, Cos(8pi/3)=1/2.
..
sin (5pi/3)
Think (5pi/3) as 1+2/3 pi
In this case you rotate 1 pi to 180 deg with two pi/3 or 120 deg to go. This puts the terminating side at 300 deg,with the same reference angle as the cos above. Hence, Sin (5pi/3)=-sqrt(3)/2 (sin is negative in the 4th quadrant)
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