SOLUTION: what is the exact value of sin(11pi/12)

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Question 669253: what is the exact value of sin(11pi/12)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
what is the exact value of sin(11pi/12)
There are 6 different ways we can go about this 
since 11pi%2F12 can be written in as the sum or difference
of special angles in these 6 ways:

11pi%2F12%29+=+%7B%7B%7B7pi%2F4-5pi%2F6 = 7pi%2F4-5pi%2F6 = 5pi%2F4-pi%2F3 = pi%2F6%2B3pi%2F4 = 2pi%2F3%2Bpi%2F4 = 5pi%2F3-3pi%2F4 = 7pi%2F6-pi%2F4

I'll pick one arbitrarily, say

11pi%2F12 = 2pi%2F3%2Bpi%2F4

sin%2811pi%2F12%29 = sin%282pi%2F3%2Bpi%2F4%29 

We use the formula:

sin%28alpha%2Bbeta%29=sin%28alpha%29cos%28beta%29%2Bcos%28alpha%29sin%28beta%29

sin%2811pi%2F12%29 = sin%282pi%2F3%2Bpi%2F4%29 = sin%282pi%2F3%29cos%28pi%2F4%29%2Bcos%282pi%2F3%29sin%28pi%2F4%29 = 
%28sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29%2B%28-1%2F2%29%28sqrt%282%29%2F2%29 = sqrt%286%29%2F4-sqrt%282%29%2F4 = %28sqrt%286%29-sqrt%282%29%29%2F4 

Edwin