SOLUTION: Find the exact value using a sum or difference identity. Some simplifications may involve using symmetry and the formulas for negatives. cos (5pi/12)

Algebra ->  Finance -> SOLUTION: Find the exact value using a sum or difference identity. Some simplifications may involve using symmetry and the formulas for negatives. cos (5pi/12)      Log On


   

Question 1079977: Find the exact value using a sum or difference identity. Some simplifications may involve using symmetry and the formulas for negatives.
cos (5pi/12)
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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5pi%2F12 = 75° = 45° + 30° = pi%2F4+%2B+pi%2F6  =====>

cos%285pi%2F12%29 = cos%28pi%2F4+%2B+pi%2F6%29  = cos%28pi%2F4%29%2Acos%28pi%2F6%29+-+sin%28pi%2F4%29%2Asin%28pi%2F6%29  ====>


    Use cos%28pi%2F4%29 = sqrt%282%29%2F2,  cos%28pi%2F6%29 = sqrt%283%29%2F2,  sin%28pi%2F4%29 = sqrt%282%29%2F2,  sin%28pi%2F6%29 = 1%2F2  ====>


= %28sqrt%282%29%2F2%29%2A%28sqrt%283%29%2F2%29+-+%28sqrt%282%29%2F2%29%2A%281%2F2%29 = sqrt%286%29%2F4+-+sqrt%282%29%2F4 = %28sqrt%286%29-sqrt%282%29%29%2F4.