SOLUTION: Determine the exact value of cos19π/12. Link to equation composition: https://gyazo.com/d7755bad6f1fbcbd33326a285055204f

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Question 1205303: Determine the exact value of cos19π/12.
Link to equation composition: https://gyazo.com/d7755bad6f1fbcbd33326a285055204f
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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Determine the exact value of cos19π/12.
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19pi%2F12%29 = 18pi%2F12 + pi%2F12.


Therefore,

    cos%2819pi%2F12%29 = cos%2818pi%2F12+%2B+pi%2F12%29 = cos%2818pi%2F12%29%2Acos%28pi%2F12%29 - sin%2818pi%2F12%29%2Asin%28pi%2F12%29 = 

  = cos%283pi%2F2%29%2Acos%28pi%2F12%29 - sin%283pi%2F2%29%2Asin%28pi%2F12%29 = 0%2Acos%28pi%2F12%29 - %28-1%29%2Asin%28pi%2F12%29 = sin%28pi%2F12%29.


Next, pi%2F12 = %28%28pi%2F6%29%29%2F2.


Therefore,  sin%28pi%2F12%29 = sqrt%28%281+-+cos%28pi%2F6%29%29%2F2%29 = sqrt%28%281+-sqrt%283%29%2F2%29%2F2%29 = sqrt%28%28%282-sqrt%283%29%29%2F2%29%2F2%29 = sqrt%282-sqrt%283%29%29%2F2%29.  


Combining everything together, we get the 


ANSWER.  cos%2819pi%2F12%29 = sqrt%282-sqrt%283%29%29%2F2%29.

Solved.