SOLUTION: sin75 degree=?

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Question 151157: sin75 degree=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sin%2875%29 Start with the given expression.


sin%2845%2B30%29 Rewrite 75 as 45+30. Take note that 45 and 30 are angles found on the unit circle.


sin%2845%29cos%2830%29%2Bcos%2845%29sin%2830%29 Expand the expression using the Sum-Difference identity



%28sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29%2B%28sqrt%282%29%2F2%29%281%2F2%29 Evaluate sin%2845%29 to get sqrt%282%29%2F2. Evaluate cos%2830%29 to get sqrt%283%29%2F2. Evaluate cos%2845%29 to get sqrt%282%29%2F2. Evaluate sin%2830%29 to get 1%2F2



sqrt%286%29%2F4%2Bsqrt%282%29%2F4 Multiply


%28sqrt%286%29%2Bsqrt%282%29%29%2F4 Add the fractions.


So sin%2875%29=%28sqrt%286%29%2Bsqrt%282%29%29%2F4