My homework is to find the sin or cos value of angle that is not directly known on the unit circle. So of course we are given an equation which adds or subracts known values to get the desired one. The problem is that I dont think memorizing them is helping me learn. I want to know how the sin(75) = sin(35+45) without readily memorizing them. So far what I did was draw a 30 degree triangle on the unit circle and then adjacent to the hypotenouse, I drew the 45 degree triangle. Then I drew a 75 degree triangle and tried to reason it through from the there but its not working. So can someone clarify why these identities work.