SOLUTION: simplify the expression: sin5pie/3 cos5pie/3-cos5pie/3 sin pie/3

Question 600374: simplify the expression: sin5pie/3 cos5pie/3-cos5pie/3 sin pie/3
Found 2 solutions by mamiya, Alan3354:
Answer by mamiya(56) (Show Source): You can put this solution on YOUR website!
you say sin(5pie/3) cos(5pie/3)-cos(5pie/3) sin (pie/3), but i think the question was rather
sin(5pie/3) cos(pie/3)-cos(5pie/3) sin (pie/3)
And if the question was what i just wrote , you do it this way.
first let take a look a those trigonometric formulas
sin(a+b) = sin(a) cos(b) + sin(b) cos(a)
sin(a-b) = sin(a) cos(b) - sin(b) cos(a)
Cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
Cos(a-b) = cos(a) cos(b) + sin(a) sin(b)

Now, let's get back to our problem
let's call 5pie/3 a and call pie/3 b
Then, sin5pie/3 cospie/3-cos5pie/3 sin pie/3= sin (a) cos(b)- cos(a) sin(b),
This looks like the second formula up above
so we get sin5pie/3 cospie/3-cos5pie/3 sin pie/3 = Sin ( a-b)
and we know for this case that a = 5pie\3 and b=pie/3
so, sin5pie/3 cospie/3-cos5pie/3 sin pie/3 = Sin ( 5pie/3 - pie/3)
= sin ( 4pie/3)
= -(sqrt(3))/2
So the anwer is Sin( 4pie/3) and if you want to go further and find its value it is -(sqrt(3))/2

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
simplify the expression: sin5pie/3 cos5pie/3-cos5pie/3 sin pie/3
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It's the Greek letter pi, not the dessert, pie.

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