SOLUTION: sin105 degree=?

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Question 151156: sin105 degree=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28105%29 Start with the given expression.


sin%2860%2B45%29 Rewrite 105 as 60+45. Take note that 60 and 45 are angles found on the unit circle.


sin%2860%29cos%2845%29%2Bcos%2860%29sin%2845%29 Expand the expression using the Sum-Difference identity



%28sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29%2B%281%2F2%29%28sqrt%282%29%2F2%29 Evaluate sin%2860%29 to get sqrt%283%29%2F2. Evaluate cos%2845%29 to get sqrt%282%29%2F2. Evaluate cos%2860%29 to get 1%2F2. Evaluate sin%2845%29 to get sqrt%282%29%2F2



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


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


So sin%28105%29=%28sqrt%286%29%2Bsqrt%282%29%29%2F4


Note: this may look oddly familiar, but it turns out that the very nature of trig is that it is very cyclical. So it is not uncommon to get the same answer given different angles.