SOLUTION: Oh God, Please Help I am so confused. Evaluate sin^2 pi/3+ cos^2 pi/6 - sin^2 5pi/3.

Algebra ->  Trigonometry-basics -> SOLUTION: Oh God, Please Help I am so confused. Evaluate sin^2 pi/3+ cos^2 pi/6 - sin^2 5pi/3.      Log On


   

Question 181075: Oh God, Please Help I am so confused.
Evaluate
sin^2 pi/3+ cos^2 pi/6 - sin^2 5pi/3.
Answer by eperette(173) About Me  (Show Source):
You can put this solution on YOUR website!
In order to do this problems you must know the values of your special angles, otherwise you will keep having lots of trouble:
sin 0 = 0
sin30=1/2
sin45= sqr(2)/2
sin60 = sqr (3)/2
sin 90 = 1
cos 0 =1
cos30 = sqr(3)/2
cos45= sqr(2)/2
cos60 = 1/2
cos90= 0
Also you must know that pi = 180 degrees....so pi/3 = 180/3=60


.....NOW.....
sin^2 pi/3 + cos^2 pi/6 - sin^2 5pi/3
(sin pi/3)^2 + (cos pi/6)^2 - (sin 5pi/3)^2
(sin 180/3)^2 + (cos 180/6)^2 - (sin 5(180)/3)^2
(sin 60)^2 + (cos 30)^2 - (sin 300)^2
(sqr(3)/2)^2 + (sqr(3)/2)^2 - (-sqr(3)/2)^2
3/4 + 3/4 - 3/4
3/4
Note: to find the value of sin 300 you must first find the reference angle of angle 300 which is 60.....and remember that angle 300 lies on the IV quadrant...
therefore sin300= -sin60