SOLUTION: Evaluate: sin 2pi cos pi/3 - cos 2pi sin pi/3
P.S. the answer is -square root of 3/2 but I don't know the right solution
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Question 677589: Evaluate: sin 2pi cos pi/3 - cos 2pi sin pi/3
P.S. the answer is -square root of 3/2 but I don't know the right solution
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
One way to do this takes advantage of the fact that all the angles in the expression are special angles. You should know (or learn) that:
Substituting these values into your expression:
which simplifies to:
Another way to do this uses the fact that the expression matches the pattern of the right side of:
with the "A" being and the "B" being . Using the formula we can rewrite your expression as sin(A-B):
We should know that the angle is an angle that terminates in the 4th quadrant and that its reference angle is . The sin of the reference angle is and since sin is negative in the 4th quadrant:
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