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Question 151157: sin75 degree=?: sin75 degree=?
Answer by jim_thompson5910(9390) About Me  (Show Source):
You can put this solution on YOUR website!
sin(75) Start with the given expression.


sin(45+30) Rewrite 75 as 45+30. Take note that 45 and 30 are angles found on the unit circle.


sin(45)cos(30)+cos(45)sin(30) Expand the expression using the Sum-Difference identity



(sqrt(2)/2)(sqrt(3)/2)+(sqrt(2)/2)(1/2) Evaluate sin(45) to get sqrt(2)/2. Evaluate cos(30) to get sqrt(3)/2. Evaluate cos(45) to get sqrt(2)/2. Evaluate sin(30) to get 1/2



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


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


So sin(75)=(sqrt(6)+sqrt(2))/4