Questions on Algebra: Trigonometry answered by real tutors!

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Question 151156: sin105 degree=?: sin105 degree=?
Answer by jim_thompson5910(9391) About Me  (Show Source):
You can put this solution on YOUR website!
sin(105) Start with the given expression.


sin(60+45) Rewrite 105 as 60+45. Take note that 60 and 45 are angles found on the unit circle.


sin(60)cos(45)+cos(60)sin(45) Expand the expression using the Sum-Difference identity



(sqrt(3)/2)(sqrt(2)/2)+(1/2)(sqrt(2)/2) Evaluate sin(60) to get sqrt(3)/2. Evaluate cos(45) to get sqrt(2)/2. Evaluate cos(60) to get 1/2. Evaluate sin(45) to get sqrt(2)/2



sqrt(6)/4+sqrt(2)/4 Multiply


(sqrt(6)+sqrt(2))/4 Add the fractions.


So sin(105)=(sqrt(6)+sqrt(2))/4


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.